Tiger Algebra/core — Serbian @ Weblate: Raising to a power, or exponentiation, is the process of …

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Raising to a power, or exponentiation, is the process of multiplying a base value b by itself the number of times given by the exponent n in the term b^n.
 
So, for example, <math>3^4</math> is the same as <math>3 x 3 x 3 x 3</math>, which equals <math>81</math>.
 
This is spoken as “three to the fourth power” or “three to the fourth”. There are two exceptions to this: The power of two is generally called “squared” so <math>3^2</math> is “three squared”. The power of three is referred to as “cubed” so <math>3^3</math> is “three cubed”.
 
Exponents are especially useful when dealing with variables, such as <math>x^3</math>. There are a few rules in simplifying several variables raised to a power in one expression.
 
When two terms with the same base are multiplied, the exponents are added:
<math>(b^n)(b^m) = b^(n+m)</math>
 
When raising a power to a power, the exponents are multiplied with each other:
<math>(b^n)^m = b^(n*m)</math>
In other words, if the entire expression <math>b^n</math> is raised to the power of <math>^m</math>, the new power of b is the product of n multiplied by m.
 
Any number to the power of zero equals 1, as long as the base value itself is not 0.
 
Enter your problem into Tiger’s calculator and the step-by-step solution will help you understand how to raise a number or an expression to a power.

Serbian

Stepenovanje ili potenciranje je postupak množenja osnovne vrednosti b samim sobom onoliko puta koliko je eksponent n dat u članu b^n.
 
Tako je, na primer, <math>3^4</math> isto što i <math>3 x 3 x 3 x 3</math>, što je jednako <math>81</math>.
 
Ovo se govori kao „tri podignuto na četvrti eksponent“ ili „tri na četvrti”. Postoje dva izuzetka od toga: Eksponent dva se obično naziva „na kvadrat“, pa je <math>3^2</math> „na kvadrat“. Eksponent trojke naziva se „na treći“, tako da je <math>3^3</math> „na treći“.
 
Eksponenti su posebno korisni kada se radi o promenljivim, kao što je <math>x^3</math>. Postoji nekoliko pravila za pojednostavljivanje nekoliko promenljivih podignutih u stepen u jednom izrazu.
 
Kada se pomnože dva člana sa istom osnovom, dodaju se eksponenti:
<math>(b^n)(b^m) = b^(n+m)</math>
 
Pri podizanju eksponenta u stepen, eksponenti se međusobno množe:
<math>(b^n)^m = b^(n*m)</math>
Drugim rečima, ako se celokupan izraz 
<math>b^n</math> podigne na stepen <math>^m</math>, nov eksponent b je proizvod n pomnožen sa m.
 
Bilo koji broj sa nulom jednak je 1, sve dok sama osnovna vrednost nije 0.
 
Unesi svoj problem u Tiger kalkulator i korak po korak rešenje će ti pomoći da razumeš kako podići broj ili izraz u stepen.

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Key	English	Serbian
PercentContent	Percentages are ratios, meaning they represent parts of a whole. The word "cent" comes from the Latin word "centum" which means "hundred," so when we say "per_cent", we actually mean per one hundred. For example, five percent, written as 5% is five per, or "out of", one hundred. Another way to express the ratio is as a fraction, in this case, <math>5/100</math>, which can be turned into a percentage by dividing the part by the whole. Dividing <math>5/100</math> would give us 0.05 or 5%. Percentages can also be bigger than the whole. For example, 120 percent (120%) is 120 out of a hundred.<br><br>But what about when we want to figure out the exact number that a percentage represents? For example, if we know that 5% of the students in our class got A's on a test and we know that there are twenty students in the class, how do we figure out how many students in the class got A's? Our first clue is that there are a total of twenty students in the class, meaning twenty is equal to 100%. If 5% is equal to <math>5/100</math> and we are looking for 5% of twenty, then we can simply multiply <math>5/100</math> by twenty to get the answer, one. So, one student in the class got an A on their test. It is worth noting that we could have also gotten the result by first converting <math>5/100</math> to a decimal, by dividing five by one-hundred and multiplying the result, 0.05, by twenty.	Procenti su odnosi, što znači da predstavljaju delove celine. Reč "cent" dolazi od latinske reči "centum" što znači "sto", tako da kada kažemo "procenat", zapravo mislimo na sto. Na primer, pet odsto, napisano kao 5% je pet po, ili "od", sto. Drugi način da se izrazi odnos je kao razlomak, u ovom slučaju, <math>5/100</math>, koji se može pretvoriti u procenat deljenjem dela sa celinom. Deljenje <math>5/100</math> bi nam dalo 0,05 ili 5%. Procenti mogu biti i veći od celine. Na primer, 120 odsto (120%) je 120 od sto.<br><br>Ali šta je kada želimo da utvrdimo tačan broj koji predstavlja procenat? Na primer, ako znamo da je 5% učenika u našem odeljenju dobilo A na testu i znamo da ima dvadeset učenika u razredu, kako da izračunamo koliko je učenika u razredu dobilo A? Naš prvi trag je da u razredu ima ukupno dvadeset učenika, što znači da je dvadeset jednako 100%. Ako je 5% jednako <math>5/100</math>, a mi tražimo 5% od dvadeset, onda možemo jednostavno da pomnožimo <math>5/100</math> sa dvadeset da dobijemo odgovor, a to je jedan. Dakle, jedan učenik u razredu je dobio A na testu. Vredi napomenuti da smo i mi mogli dobiti rezultat prvo konverzijom <math>5/100</math> na decimalu, deljenjem pet sa sto i množenjem rezultata, 0,05, sa dvadeset.
Pi	Pi	Pi
PiTopic	Pi	Pi
PiContent	<div style="white-space: normal;"> <p>Pi (<math>\pi</math>) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a finite decimal or a fraction.</p> <h2>Value of Pi</h2> <p>The value of pi is approximately 3.14159, but it is an infinitely long decimal with no repeating pattern. It is often approximated as <math>\pi \approx 3.14</math> for practical calculations.</p> <h2>Properties of Pi</h2> <ul> <li>Pi is a transcendental number, meaning it is not the root of any non-zero polynomial equation with rational coefficients.</li> <li>It is involved in many mathematical formulas and equations, including those in geometry, trigonometry, calculus, and physics.</li> <li>Pi is an important constant in the field of mathematics and has been studied and approximated for thousands of years.</li> </ul> <h2>History</h2> <p>The ancient Egyptians and Babylonians were among the first civilizations to approximate the value of pi. However, it was the Greek mathematician Archimedes who provided one of the earliest rigorous approximations of pi using inscribed and circumscribed polygons.</p> <p>The symbol <math>\pi</math> was first used by Welsh mathematician William Jones in 1706, and it was popularized by Swiss mathematician Leonhard Euler in the 18th century.</p> <p>Pi has since become one of the most well-known and studied mathematical constants, with its digits computed to trillions of decimal places using modern computational techniques.</p> </div>	Broj Pi je matematička konstanta, odnos opsega kružnice i njenog prečnika, obično aproksimiran na 3,14159.
PolynomialLongDivision	Polynomial long division	Polinomno dugo deljenje
PolynomialLongDivisionContent	<div style="white-space: normal;"> <p>Polynomial long division is a method used to divide polynomials, similar to long division with numbers. It allows us to divide one polynomial by another polynomial to find the quotient and remainder.</p> <h2>Step-by-Step Process</h2> <p>To perform polynomial long division, follow these steps:</p> <ol> <li>Arrange the terms of the dividend and divisor in descending order of their degrees.</li> <li>Divide the leading term of the dividend by the leading term of the divisor to obtain the first term of the quotient.</li> <li>Multiply the entire divisor by the first term of the quotient, and subtract this product from the dividend.</li> <li>Bring down the next term of the dividend, and repeat steps 2 and 3 until all terms have been processed.</li> <li>The resulting expression is the quotient, and any remaining terms constitute the remainder.</li> </ol> <h2>Example</h2> <p>Let's perform polynomial long division for the division <math>(2x^3 + 3x^2 - 4x + 1) ÷ (x - 1)</math>:</p> <ol> <li>Dividend: <math>2x^3 + 3x^2 - 4x + 1</math></li> <li>Divisor: <math>x - 1</math></li> <li>Quotient: <math>2x^2 + 5x + 1</math></li> <li>Remainder: <math>0</math></li> </ol> <p>Therefore, <math>(2x^3 + 3x^2 - 4x + 1) ÷ (x - 1) = 2x^2 + 5x + 1</math>.</p> <p>Polynomial long division is a powerful tool for simplifying polynomial expressions and solving equations.</p> </div>	U algebri, polinomno dugo deljenje je algoritam za podelu polinoma drugim polinomom istog ili nižeg stepena, uopštenom verzijom poznate aritmetičke tehnike koja se naziva duga podela. To se lako može uraditi ručno, jer inače složeni problem podele razdvaja na manje. Ponekad je korišćenje skraćene verzije zvane sintetička podela brže, sa manje pisanja i manje proračuna. Druga skraćena metoda je polinomska kratka podela (Blomkvist-ova metoda).
PolynomialRootCalculator	Polynomial root calculator	Računanje korena polinoma
PolynomialRootCalculatorContent	Polynomial roots (zeroes) are calculated by applying a set of methods aimed at finding values of n for which f(n)=0. One method uses the Rational Root (or Rational Zero) Test. This is also be referred to as the Rational Root (or Rational Zero) Theorem or the p/q theorem. Regardless of its name, it only finds rational roots that are the number n that can be expressed as the quotient of two integers. <br><br> The Rational Root Theorem states that if a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the trailing constant a0 and q is a factor of the leading coefficient an. When the leading coefficient is 1, the possible rational zeros are the factors of the constant term. <br><br> Enter your problem into Tiger’s calculator and the step-by-step solution will help you understand how find the roots of a polynomial.	Koreni polinoma (nule) izračunavaju se primenom skupa metoda usmerenih na pronalaženje vrednosti n za koje je f(n) = 0. Jedna metoda koristi test racionalnog korena (ili racionalne nule). Ovo se takođe naziva i Teorema racionalnog korena (ili racionalne nule) ili p/q teorema. Bez obzira na ime, pronalazi samo racionalne korene koji su broj n koji se može izraziti kao količnik dve celobrojne vrednosti. <br><br> Teorija racionalnog korena kaže da ako polinom ima celobrojne koeficijente, tada svaka racionalna nula f(x) ima oblik p/q gde je p faktor prateće konstante a0, a q faktor vodećeg koeficijenta an. Kada je vodeći koeficijent 1, moguće racionalne nule su faktori konstantnog člana. <br><br> Unesi svoj problem u Tigrov kalkulator i rešenje dato korak po korak će ti pomoći da razumeš kako pronaći korene polinoma.
Powersofi	Powers of i	i eksponenti
PowersofiContent	Imaginary numbers, almost always written as i, are unique in that they equal a negative number when multiplied by themselves. You might be wondering how this is possible since even negative numbers multiplied by themselves equal a positive number. The trick is that <math>i=√-1</math>, which, when multiplied by itself, removes the radical symbol but does not change the symbol of the number inside the radical symbol.<br><br>What is even more interesting about imaginary numbers, is that raising them by increasing powers results in a predictable, repetitive cycle that helps us quickly solve problems that might otherwise be unruly. For example, we can use this cycle to quickly solve <math>i^3473</math>, which might otherwise require a lot of extra work. Here is how it works: i, when raised to the powers of 0 through 3, results in different outcomes. After this, however, the outcomes start to repeat themselves every four digits, forever. So, <math>i^0 = i^4 = i^8 = 1</math> and <math>i^3 = i^7 = i^11 = -i</math> and so on.<br> <img src="/images/powerofi-graph1.png" alt="Power Of I"><br><br> This means that, instead of manually calculating i raised to any power higher than 4, we can find a number close to that power and use the pattern described above, as well as properties of exponents, to simplify it.<br><br> For example, let's <a target="_blank" href="https://www.tiger-algebra.com/en/solution/power-of-i/i%5E23/">calculate <math>i^23</math></a>	Imaginarni brojevi, skoro uvek napisani kao i, jedinstveni su po tome što su jednaki negativnom broju kada se pomnože sami sa sobom. Možda se pitate kako je to moguće jer su čak i negativni brojevi pomnoženi sami sa sobom jednaki pozitivnom broju. Trik je u tome da <math>i=√-1</math> koji, kada se pomnoži sam sa sobom, uklanja radikalni simbol, ali ne menja simbol broja unutar radikalnog simbola.<br><br>Ono što je još zanimljivije u vezi sa imaginarnim brojevima je da njihovo potenciranje rezultira predvidljivim ponavljajućim ciklusom i koji nam pomaže da brzo rešimo probleme koji bi inače mogli biti van kontrole. Na primer, možemo koristiti ovaj ciklus za brzo rešavanje <math>i^3473</math>, što bi inače zahtevalo mnogo dodatnog rada. Evo kako to funkcioniše: kada se 'i' podigne na stepen od 0 do 3, rezultira različitim ishodima. Međutim, nakon ovoga se ishodi počinju ponavljati na svake četiri cifre, zauvek. Dakle, <math>i^0 = i^4 = i^8 = 1</math> i <math>i^3 = i^7 = i^11 = -i</math> i tako dalje.<br> <img src="/images/powerofi-graph1.png" alt="Power Of I"><br><br> To znači da, umesto ručnog izračunavanja i podignutog na bilo koji stepen veći od 4, možemo pronaći broj blizu tom stepenu i koristiti opisani obrazac, kao i osobine eksponenata, da ga pojednostavimo.<br><br>Na primer, izračunajmo <math>i^23</math> <a href="/en/solution/power-of-i/I%5E23/">LINK i^23</a>
PropertiesofaStraightLine	Properties of a straight line	Osobine prave linije
PropertiesofaStraightLineTopicContent	A straight line is a one-dimensional figure that has a minimal thickness and extends infinitely in two opposing directions.<br> Every straight line has a slope that represents its gradient, or steepness. In mathematical expressions, this is typically written as <math>m</math> and we can calculate it by selecting two points on the line and dividing the difference in their y-coordinates by the difference in their x-coordinates. The change in a line's y-coordinates represents the line's vertical change and is often referred to as the "rise", whereas the change in a line's x-coordinates represents the line's horizontal change and is often referred to as the "run". This means the slope of a straight line is equal to the line's rise divided by its run <math>m =(y_2-y_1)/(x_2-x_1)=△y/△x</math>. <br><br> Here are some other useful facts about straight lines: <br> <ul> <li>A straight line is the shortest distance between any two points.</li> <li>If a line rises to the right, then its slope is positive.</li> <li>If a line falls to the right, then its slope is negative.</li> <li>A line that rises to the right at a 45° angle has a slope of 1.</li> <li>A line that falls to the right at a 45° angle has a slope of -1.</li> <li>A horizontal line has a slope of 0.</li> <li>A vertical line has an undefined slope.</li> </ul> <br> <img src="/images/solver/Properties_of_straight_line_firs_image.png" alt="Properties of straight lines"/> <br> <br> <b>Types of lines:</b> <ul> <li>Ray: A line with one fixed end and one end that continues forever.</li> <li>Line segment: A line with two fixed ends.</li> <li>Parallel lines: Two or more lines that have the same slope and, therefore, never meet.</li> <li>Perpendicular lines: Two lines that intersect at a right angle (90°). Their slopes are negative reciprocals of one another.</li> <li>Vertical line: A line that runs parallel to a plane's y-axis. The slope of a vertical line is undefined.</li> <li>Horizontal line: A line that runs parallel to a plane's x-axis. The slope of a vertical line is 0.</li> <li>Transversal: A line that crosses at least two other lines.</li> <li>Tangent line: A line that touches a curve, matching the curve's slope at that point.</li> <li>Secant line: A line that intersects two or more points on a curve.</li> </ul> <br> <img src="/images/solver/Properties_of_straight_line_second_image.png" alt="Properties of straight lines 2nd image"/> <br> <b>Equations of lines:</b> A linear equation is the equation of a straight line. Linear equations most commonly take the following forms: <ul> <li><b>Standard form</b>: <math>ax+by=c</math> in which <math>x</math> and <math>y</math> represent the x and y-coordinates of a point on the line and <math>a, b</math> and <math>c</math> represent coefficients. If <math>a=0</math> then <math>b≠0</math> and if <math>b=0</math> then <math>a≠0</math>.</li> <li><b>Slope-intercept form</b>: <math>y=mx+b</math> in which <math>x</math> and <math>y</math> represent the coordinates of a point on the line, <math>m</math> represents the slope, and <math>b</math> represents the y-Intercept, the value of <math>y</math> when <math>x</math> equals <math>0</math>.</li> <li><b>Point-slope form</b>: <math>y-y_1=m(x-x_1)</math> in which <math>x</math> and <math>x_1</math> represent the x-coordinates of two points on a line, <math>y</math> and <math>y_1</math> represent the y-coordinates of two points on a line, and <math>m</math> represents the slope of a line.</li> <li><b>Equation of a vertical line</b>: The exception to this is when a line is vertical, in which case its slope is undefined and the line cannot be represented by slope-intercept or point-slope form. The equation of such lines is <math>x=</math>?. All the points on vertical lines have the same x-coordinate so we define the line in terms of its x-variable.</li> </ul> <b>Relevant terms:</b> <ul> <li>y-intercept: The point on a graph where a line crosses the graph's y-axis. It is also the value of <math>y</math> when <math>x</math> equals <math>0</math>.</li> <li>x-Intercept: The point on a graph where a line crosses the graph's x-axis. It is also the value of <math>x</math> when <math>y</math> equals <math>0</math>.</li> </ul>	Prava linija je jednodimenzionalna figura koja ima minimalnu debljinu i proteže se beskonačno u dva suprotna smera.<br> Svaka prava linija ima nagib koji predstavlja njen gradijent, odnosno strminu. U matematičkim izrazima, ovo se obično piše kao <math>m</math> i možemo ga izračunati odabirom dve tačke na pravoj i deljenjem razlike njihovih y-koordinata sa razlikom njihovih x-koordinata. Promena u y-koordinatama linije predstavlja vertikalnu promenu linije i često se naziva "uspon", dok promena u x-koordinatama linije predstavlja horizontalnu promenu linije i često se naziva "trčanje". To znači da je nagib ravne linije jednak porastu linije podeljenom sa kretanjem <math>m =(y_2-y_1)/(x_2-x_1)=△y/△x</math>. <br><br> Evo još nekih korisnih činjenica o pravim linijama: <br> <ul> <li>Prava linija je najkraće rastojanje između bilo koje dve tačke.</li> <li>Ako se linija uzdiže udesno, tada je njen nagib pozitivan.</li> <li>Ako linija pada udesno, tada je njen nagib negativan.</li> <li>Linija koja se uzdiže udesno pod uglom od 45° ima nagib od 1.</li> <li>Prava koja pada udesno pod uglom od 45° ima nagib -1.</li> <li>Horizontalna linija ima nagib 0.</li> <li>Vertikalna linija ima nedefinisan nagib.</li> </ul> <br> <img src="/images/properties-of-a-straight-line-img1.png" alt="Properties of straight lines"> <br> <br> <b>Vrste linija:</b> <ul> <li>Zrak: linija sa jednim fiksnim krajem i jednim krajem koji se nastavlja zauvek.</li> <li>Segment linije: linija sa dva fiksna kraja.</li> <li>Paralelne linije: dve ili više linija koje imaju isti nagib i zbog toga se nikada ne susreću.</li> <li>Poprečne linije: dve linije koje se seku pod pravim uglom (90°). Njihovi nagibi su negativno recipročni jedni drugima.</li> <li>Vertikalna linija: linija koja ide paralelno sa y-osom ravnine. Nagib vertikalne linije je nedefinisan.</li> <li>Horizontalna linija: linija koja ide paralelno sa x-osom ravnine. Nagib horizontalne linije je 0.</li> <li>Transverzala: linija koja prelazi najmanje dve druge linije.</li> <li>Tangentna linija: linija koja dodiruje krivu, koja odgovara nagibu krive u toj tački.</li> <li>Sekanta: linija koja seče dve ili više tačaka na krivi.</li> </ul> <br> <img src="/images/properties-of-a-straight-line-img2.png" alt="Properties of straight lines"> <br> <b>Jednačine linija:</b> linearna jednačina je jednačina prave linije. Linearne jednačine najčešće imaju sledeće forme: <ul> <li><b>Standardna forma</b>: <math>ax+by=c</math> u kom <math>x</math> i <math>y</math> predstavljaju x i y-koordinate tačke na liniji i <math>a, b</math> i <math>c</math> predstavljaju koeficijente. Ako <math>a=0</math> onda <math>b≠0</math> i ako <math>b=0</math> onda <math>a≠0</math>.</li> <li><b>Forma odsečka nagiba</b>: <math>y=mx b</math> u kom <math>x</math> i <math>y</math> predstavljaju koordinate tačke na liniji, <math>m</math> predstavlja nagib, i <math>b</math> predstavlja odsečak na y osi, vrednost <math>y</math> kada <math>x</math> jednaki <math>0</math>.</li> <li><b>Forma tačka-nagib</b>: <math>y-y_1=m(x-x_1)</math> u kom <math>x</math> i <math>x_1</math> predstavljaju x-koordinate dveju tačaka na liniji, <math>y</math> i <math>y_1</math> predstavljaju y-koordinate dveju tačaka na liniji i <math>m</math> predstavlja nagib linije.</li> <li><b>Jednačina vertikalne linije</b>: izuzetak od ovoga je kada je linija vertikalna, u kom slučaju je njen nagib nedefinisan i linija ne može biti predstavljena u obliku nagib-odsečak ili tačka-nagib. Jednačina takvih linija je <math>x=</math>?. Sve tačke na vertikalnim linijama imaju istu x-koordinatu, tako da liniju definišemo u smislu njene x-varijable.</li> </ul> <b>Relevantni pojmovi:</b> <ul> <li>Odsečak na y osi: tačka na grafikonu gde linija prelazi y osu grafikona. To je takođe vrednost <math>y</math> kada je <math>x</math> jednako <math>0</math>.</li> <li>Odsečak na x osi: tačka na grafikonu u kojoj linija prelazi x osu grafikona. To je takođe vrednost <math>x</math> kada je <math>y</math> jednako <math>0</math>.</li> </ul>
PullingOutLikeTerms	Pulling out like terms	Izvlačenje sličnih članova
PullingOutLikeTermsContent	<div style="white-space: normal;"> <p>When simplifying algebraic expressions, one of the fundamental techniques is pulling out like terms. Like terms are those that have the same variables raised to the same powers. Here's how you can do it:</p> <h2>Step 1: Identify Like Terms</h2> <p>Scan through the expression and identify terms that have the same variables and the same powers. For example, in the expression <math>3x + 2y - 5x + 4y</math>, the terms <math>3x</math> and <math>-5x</math> are like terms because they both have the variable <math>x</math> raised to the power of 1.</p> <h2>Step 2: Combine Like Terms</h2> <p>Once you've identified like terms, you can combine them by adding or subtracting their coefficients. For example, in the expression <math>3x + 2y - 5x + 4y</math>, combining the like terms gives us <math>(3x - 5x) + (2y + 4y)</math>, which simplifies to <math>-2x + 6y</math>.</p> <h2>Step 3: Simplify the Expression</h2> <p>After combining like terms, simplify the expression further if possible. In our example, <math>-2x + 6y</math> cannot be simplified any further because there are no more like terms to combine.</p> <p>Remember, pulling out like terms is crucial for simplifying algebraic expressions and making them easier to work with.</p> </div>	U algebri, slični članovi su članovi koji imaju iste varijable i eksponente. Tiger Algebra rešavač pomaže vam da lako pronađete i grupišete slične članove pokazujući vam rešenja korak po korak.
RaisingtoaPower	Raising to a power	Stepenovanje
RaisingtoaPowerContent	Raising to a power, or exponentiation, is the process of multiplying a base value b by itself the number of times given by the exponent n in the term b^n. <br><br> So, for example, <math>3^4</math> is the same as <math>3 x 3 x 3 x 3</math>, which equals <math>81</math>. <br><br> This is spoken as “three to the fourth power” or “three to the fourth”. There are two exceptions to this: The power of two is generally called “squared” so <math>3^2</math> is “three squared”. The power of three is referred to as “cubed” so <math>3^3</math> is “three cubed”. <br><br> Exponents are especially useful when dealing with variables, such as <math>x^3</math>. There are a few rules in simplifying several variables raised to a power in one expression. <br><br> When two terms with the same base are multiplied, the exponents are added: <math>(b^n)(b^m) = b^(n+m)</math> <br><br> When raising a power to a power, the exponents are multiplied with each other: <math>(b^n)^m = b^(n*m)</math> In other words, if the entire expression <math>b^n</math> is raised to the power of <math>^m</math>, the new power of b is the product of n multiplied by m. <br><br> Any number to the power of zero equals 1, as long as the base value itself is not 0. <br><br> Enter your problem into Tiger’s calculator and the step-by-step solution will help you understand how to raise a number or an expression to a power.	Stepenovanje ili potenciranje je postupak množenja osnovne vrednosti b samim sobom onoliko puta koliko je eksponent n dat u članu b^n. <br><br> Tako je, na primer, <math>3^4</math> isto što i <math>3 x 3 x 3 x 3</math>, što je jednako <math>81</math>. <br><br> Ovo se govori kao „tri podignuto na četvrti eksponent“ ili „tri na četvrti”. Postoje dva izuzetka od toga: Eksponent dva se obično naziva „na kvadrat“, pa je <math>3^2</math> „na kvadrat“. Eksponent trojke naziva se „na treći“, tako da je <math>3^3</math> „na treći“. <br><br> Eksponenti su posebno korisni kada se radi o promenljivim, kao što je <math>x^3</math>. Postoji nekoliko pravila za pojednostavljivanje nekoliko promenljivih podignutih u stepen u jednom izrazu. <br><br> Kada se pomnože dva člana sa istom osnovom, dodaju se eksponenti: <math>(b^n)(b^m) = b^(n+m)</math> <br><br> Pri podizanju eksponenta u stepen, eksponenti se međusobno množe: <math>(b^n)^m = b^(n*m)</math> Drugim rečima, ako se celokupan izraz <math>b^n</math> podigne na stepen <math>^m</math>, nov eksponent b je proizvod n pomnožen sa m. <br><br> Bilo koji broj sa nulom jednak je 1, sve dok sama osnovna vrednost nije 0. <br><br> Unesi svoj problem u Tiger kalkulator i korak po korak rešenje će ti pomoći da razumeš kako podići broj ili izraz u stepen.
ReducingFractionsToLowestTerms	Reducing fractions to lowest terms	Smanjenje razlomaka na najniže članove
ReducingFractionsToLowestTermsContent	A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. For example, if we examine the fraction <math>25/50</math>, we can reduce this fraction by dividing both the numerator and denominator by their common factor, 25. <math>25/25=1</math> and <math>50/25=2</math> then <math>25/50=1/2</math>. which is a fraction in its lowest terms.	Razlomak je najmanji član kada brojilac i nazivnik nemaju zajednički delilac osim 1. Na primer, ako ispitamo razlomak <math>25/50</math>, taj razlomak možemo smanjiti deljenjem brojioca i imenioca njihovim zajedničkim deliocem, 25. <math>25/25=1</math> i <math>50/25=2</math> tada <math>25/50=1/2</math>. što je razlomak skraćen na najniže članove.
SimplifyingRadicals	Simplifying radicals	Pojednostavljivanje radikala
SimplifyingRadicalsContent	A Square Root Radical is said to be simplified, or in its simplest form, when the radicand has no square factors. <br><br> Consider <math>sqrt(55)</math>, for example, has no square factors. Its factors are 5 and 11 <math>(511=55)</math>, neither of which is a square number. Therefore, it is in its simplest form. <br><br> In contrast <math>sqrt(200)</math>, has the square factor 100. <math>(200 = 100 2)</math>. Therefore, it is not in its simplest form. To get the simplest form <math>sqrt(200)=sqrt(100)sqrt(2)=10sqrt(2)</math>	Za kvadratni koren radikal se kaže da je pojednostavljen, ili u svom najprostijem obliku, kada radikand nema kvadratne faktore. <br><br> Ukoliko <math>kvadratni koren(55)</math>, na primer, nema kvadratne faktore. Njegovi faktori su 5 i 11 <math>(511=55)</math>, od kojih nijedan nije kvadratni broj. Stoga je u svom najjednostavnijem obliku. <br><br> Nasuport tome <math>kvadratni koren(200)</math>, ima faktor kvadrata 100. <math>(200 = 100 2)</math>. Stoga nije u najprostijem obliku. Da biste dobili najprostiji oblik <math>kvadratni koren(200)=kvadratni koren(100)kvadratni koren(2)=10kvadratni koren(2)</math>
NonLinearEquations	Nonlinear equations	Nelinearne jednačine
NonLinearEquationsContent	A nonlinear equation is also known as a polynomial equation. An equation that has a degree (or exponent) higher than 1 is considered nonlinear. Such equations are defined by equating polynomials (of a degree greater than one) to zero. They are differentiated from linear equations by evaluating the relationship between variables: when one variable (x) does not cause the other variable (y) to increase or decrease in a way corresponding to the slope’s value, it is nonlinear. When graphed, nonlinear equations may have the form of a parabola, a curved X shape, or some variation of these curved forms. It never, however, takes the form of a line, hence its name. <div style="white-space: normal;"> <h2>Types of Nonlinear Equations</h2> <p>There are various types of nonlinear equations, including:</p> <ul> <li><strong>Polynomial equations:</strong> Equations where the unknowns are raised to integer powers.</li> <li><strong>Exponential equations:</strong> Equations involving exponential functions, such as <math>e^x</math> or <math>a^x</math>.</li> <li><strong>Trigonometric equations:</strong> Equations involving trigonometric functions like sine, cosine, or tangent.</li> <li><strong>Logarithmic equations:</strong> Equations involving logarithmic functions, such as <math>\log(x)</math> or <math>\ln(x)</math>.</li> <li><strong>Rational equations:</strong> Equations containing rational functions, where the unknowns are in the numerator or denominator of fractions.</li> </ul> <h2>Solving Nonlinear Equations</h2> <p>Solving nonlinear equations can be challenging and often requires numerical or iterative methods since closed-form solutions may not exist.</p> <p>Common techniques for solving nonlinear equations include:</p> <ul> <li>Graphical methods</li> <li>Numerical methods like Newton's method or the secant method</li> <li>Iterative methods like fixed-point iteration or the bisection method</li> </ul> <h2>Applications</h2> <p>Nonlinear equations arise in various fields, including physics, engineering, economics, and biology. They are used to model complex relationships and phenomena that cannot be described by linear equations.</p> <p>Understanding nonlinear equations and their solutions is crucial for analyzing and solving problems in many scientific and engineering disciplines.</p> </div>	Nelinearna jednačina je takođe poznata i kao polinomska jednačina. Jednačina koja ima stepen (ili eksponent) veći od 1 smatra se nelinearnom. Takve jednačine su definisane izjednačavanjem polinoma (stepena većeg od jedan) sa nulom. Razlikuju se od linearnih jednačina procenom odnosa između promenljivih: kada jedna promenljiva (x) ne uzrokuje da se druga promenljiva (y) povećava ili smanjuje na način koji odgovara vrednosti nagiba, ona je nelinearna. Kada se slikaju nelinearne jednačine mogu imati oblik parabole, zakrivljeni oblik X ili neku varijaciju ovih zakrivljenih oblika. Međutim, nikada nema oblik linije, pa je otuda i ime.
DeMoivreFormula	De Moivre formula	Moavrova formula
DeMoivreFormulaContent	De Moivre’s formula, also called de Moivre’s theorem or de Moivre’s identity, is used to determine the nth power of a complex number. It states that if n is any integer and x is a real number, then <math>(cos(x) + i sin(x))^n = cos(nx) + i sin(nx)</math>, where i is the imaginary unit <math>(i^2 = −1)</math>. The expression <math>cos(x) + i sin(x)</math> is sometimes reduced to <math>cis(x)</math>. De Moivre’s formula is a direct method for solving problems involving powers of complex numbers. In an extended form, it can be used to find the nth roots of a complex number.	Moavrova formula, koja se takođe naziva Moavrova teorema ili Moavrov identitet, koristi se za određivanje n eksponenta kompleksnog broja. Navodi se da ako je n bilo koji ceo broj i x je stvaran broj, onda je <math>(cos(x) + i sin(x))^n = cos(nx) + i sin(nx)</math>, pri čemu i je zamišljena jedinica <math>(i^2 = −1)</math>. Izraz <math>cos(x) + i sin(x)</math> ponekad se svodi na <math>cis(x)</math>. Moavrova formula je direktna metoda za rešavanje problema koji uključuju moći kompleksnih brojeva. U proširenom obliku, pomoću njega se mogu naći n-ti koreni složenog broja.
ScientificNotation	Scientific notation	Naučna notacija
ScientificNotationContent	Scientific notation, also referred to as scientific form, standard index form, or standard form, is a way of writing very large or very small numbers without having to write out every digit. This is written as a number between <math>1</math> and <math>10</math> multiplied by a power of <math>10</math> and is represented by the formula:<br> <span class="formula-look"><math>a\cdot10^b</math></span><br> In which <math>1≤a<10<math>.<br> The power that <math>10</math> is raised to can be thought of as the number of places to the right (when the power is positive) or left (when the power is negative) that the decimal point needs to move.<br><br> For example:<br> <math>5.6\cdot10^9</math> is the scientific notation of <math>5,600,000,000</math>, where the decimal point moves nine places to the right. <math>5\cdot10^-9</math> is the scientific notation of <math>0.000000005</math>, where the decimal point moves nine places to the left.	Naučna notacija se takođe naziva naučni oblik ili standardni indeksni oblik, ili u Velikoj Britaniji, standardni obrazac.
SolvingQuadraticEquationsByCompletingTheSquare	Solving quadratic equations by completing the square	Rešavanje kvadratnih jednačina dopunjavanjem kvadrata
SolvingQuadraticEquationsByCompletingTheSquareContent	Like factoring (solver coming soon) and <a target="_blank" href="https://www.tiger-algebra.com/en/terms-and-topics/solving-quadratic-equations-using-the-formula/">the quadratic formula</a>, completing the square is a method used to solve quadratic equations.<br> The standard form of a quadratic equation is <math>ax^2+bx+c=0</math> , in which <math>a</math>, <math>b</math> and <math>c</math> represent the coefficients and <math>x</math> represents an unknown variable.<br> To complete the square, we first turn the quadratic equation into a perfect square trinomial (described below) and then solve to find its square root.<br><br> So, what exactly is a perfect square trinomial? If a perfect square is the product of a number or expression that is multiplied by itself, such as <math>9</math>, which is the product of <math>3·3</math>, and a trinomial is an algebraic expression with three terms, such as <math>2x^2+4x–7</math>, then it is safe to assume a perfect square trinomial would be an algebraic expression with three terms that is also the product of a binomial multiplied by itself, such as <math>(x+4)·(x+4)=x^2+8x+16</math>.<br><br> It is important to note that if the second term of the equation, <math>bx</math>, is missing, then we cannot complete the square and need to use another method, such as <a target="_blank" href="https://www.tiger-algebra.com/en/terms-and-topics/solving-quadratic-equations-using-the-formula/">the quadratic formula</a>, to solve the equation.<br><br> Enter your quadratic equation into Tiger’s calculator and the step-by-step solution will help you understand how to solve quadratic equations by completing the square.	Kvadratne jednačine se mogu rešiti popunjavanjem kvadrata, što znači pretvaranje kvadratne jednačine u savršeni kvadratni trinom i uzimanje kvadratnog korena. <br><br> Šta je savršeni kvadratni trinom? Savršeni kvadrat je proizvod broja ili izraza koji se pomnoži sam sa sobom, kao što je savršeni kvadrat <math>9</math>, koji je proizvod <math>3x3</math>. A trinom je algebarski izraz sa tri člana, kao što je <math>2x2+4x–7</math>. Dakle, savršeni kvadratni trinom je algebarski izraz sa tri člana koji je proizvod binoma pomnoženog samoga sebe. <br><br> Unesi svoju kvadratnu jednačinu u Tiger kalkulator i korak po korak rešenje će ti pomoći da razumeš kako da rešiš kvadratne jednačine popunjavanjem kvadrata.
SolvingQuadraticEquationsUsingTheFormula	Solving quadratic equations using the quadratic formula	Rešavanje kvadratnih jednačina pomoću kvadratne formule
SolvingQuadraticEquationsUsingTheFormulaContent	The solution(s), sometimes called roots or zeros, to a quadratic equation in its standard form, <math>ax2+bx+c=0</math>, can be found by plugging the equation's coefficients, a, b, and c, into the quadratic formula:<br> <math>x=\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}</math><br> When plugged back into the original equation, these roots cause the equation to equal zero.<br><br>As the ± sign in the quadratic formula suggests, there can be two possible solutions, depending on the outcome of the formula's discriminant, <math>b^2-4ac</math>, the part of the quadratic formula under the radical symbol. The binomial, <math>b^2-4ac</math>, is called the discriminant because it discriminates between the possible solutions. <ul> <li>If <math>b^2-4ac>0</math> then the equation has two solutions.</li> <li>If <math>b^2-4ac=0</math> then the equation has one solution.</li> <li>If <math>b^2-4ac<0</math> then the equation has two complex numbers solutions. If you have not studied this topic yet, then you can probably assume there are no solutions for this equation.</li><br> <img src="/images/quadratic-equations-graph1.png" alt="Solving quadratic equations via formula">	Rešenja, koja se ponekad nazivaju koreni ili nule, kvadratne jednačine u njenom standardnom obliku, <math>ax2+bx c=0</math> se može naći dodavanjem koeficijenata jednačine, a, b i c, u kvadratnu formulu, <math>x=(-b±√(b^2-4ac))/(2a)</math>. Kada se ponovo uključe u originalnu jednačinu, ovi koreni uzrokuju da jednačina bude jednaka nuli.<br><br>Kao što znak ± u kvadratnoj formuli sugeriše, mogu postojati dva moguća rešenja, u zavisnosti od ishoda diskriminanta formule, <math>b^2-4ac</math>, deo kvadratne formule ispod radikalnog simbola. Binom, <math>b^2-4ac</math>, naziva se diskriminantnim jer pravi razliku između mogućih rešenja. <ul> <li>Ako je <math>b^2-4ac>0</math>, tada jednačina ima dva rešenja.</li> <li>Ako je <math>b^2-4ac=0</math> tada jednačina ima jedno rešenje.</li> <li>Ako je <math>b^2-4ac<0</math>, tada jednačina ima dva rešenja kompleksnih brojeva. Ako još niste proučavali ovu temu, onda verovatno možete pretpostaviti da nema rešenja za ovu jednačinu.</li><br> <img src="/images/quadratic-equations-graph1.png" alt="Solving quadratic equations via formula">
OrderOfOperations	Order of operations	Redosled operacija

Key	English	Serbian
QIVFSStep8TextUnit1	Since {Step8InequalityInput} has a {Step8Inequality} inequality sign, we look for the parabola intervals that are above the x-axis.	Pošto {Step8InequalityInput} ima znak nejednakosti {Step8Inequality}, tražimo intervale parabole iznad x-ose.
QIVFSStep8TextUnit2	Since {Step8InequalityInput} has a {Step8Inequality} inequality sign, we look for the parabola intervals that are below the x-axis.	Budući da {Step8InequalityInput} ima znak nejednakosti {Step8Inequality}, tražimo intervale parabole ispod x-ose.
QIVFSStep8TextUnit3	Solution: {Step8SolutionInequalityNotation}	Rešenje: {Step8SolutionInequalityNotation}
QIVFSStep8TextUnit4	Interval notation: {Step8SolutionIntervalNotation}	Notacija intervala: {Step8SolutionIntervalNotation}
QIVFSStep8Title1	Choose the correct interval (solution)	Pronađi ispravan interval (rešenje)
QIVFSStepFinalSpokenDescription	The final result is {SolutionFinalResult}	Konačni rezultat je {SolutionFinalResult}
QuadraticEquations	Quadratic Equations	Kvadratne jednačine
QuadraticEquationsFormattingGuide	<p>Quadratic equations with one unknown look like this:</p> <p>ax<sup>2</sup>+bx+c=0</p> <h4>Common issues:</h4> <p>Don’t forget a variable! A variable can be any letter of the Latin alphabet, such as y, w, t or R.</p> <p>For example<br> 5W<sup>2</sup>+6W+4=0</p> <p>Don’t do this:<br> 11<sup>2</sup>+25-24</p> <h3>Examples</h3> <ul> <li><a href=/en/solution/quadratic-equationsby-completing-the-square/2x%5E2-14x-120=0/">2x<sup>2</sup>-14x-120 = 0</a></li> <li><a href="/en/solution/quadratic-equationsby-completing-the-square/480-68a+2a%5E2/">480-68a+2a<sup>2</sup></a></li> <li><a href="/en/solution/quadratic-equationsby-completing-the-square/16m%5E2+8m=0/">16m<sup>2</sup>+8m=0</a></li> <li><a href="/en/solution/quadratic-equationsby-completing-the-square/9-4x%5E2=-27/">9-4x<sup>2</sup>=-27</a></li> </ul>	<p>Kvadratne jednačine sa jednom nepoznatom izgledaju ovako:</p> <p>ax<sup>2</sup>+bx+c=0</p> <h4>Česta pitanja:</h4> <p>Ne zaboravite slovo! Slovo može biti bilo koje slovo latiničnog alfabeta, poput y, w, t ili R.</p> <p>Na primer<br> 5W<sup>2</sup>+6W+4=0</p> <p>Ne radite ovo:<br> 11<sup>2</sup>+25-24</p> <h3>Primeri</h3> <ul> <li><a href=/en/solution/quadratic-equationsby-completing-the-square/2x%5E2-14x-120=0/">2x<sup>2</sup>-14x-120=0</a></li> <li><a href="/en/solution/quadratic-equationsby-completing-the-square/480-68a+2a%5E2/">480-68a+2a<sup>2</sup></a></li> <li><a href="/en/solution/quadratic-equationsby-completing-the-square/16m%5E2+8m=0/">16m<sup>2</sup>+8m=0</a></li> <li><a href="/en/solution/quadratic-equationsby-completing-the-square/9-4x%5E2=-27/">9-4x<sup>2</sup>=-27</a></li> </ul>
QuadraticEquationsViaFormulaSolver	Solving quadratic equations using the quadratic formula	Rešavanje kvadratnih jednačina pomoću kvadratne formule
QuadraticEquationsViaFormulaSolver.plugin	solving quadratic equations using the quadratic formula	rešavanju kvadratnih jednačina pomoću kvadratne formule
QuadraticInequalities	Quadratic Inequalities	Kvadratne nejednakosti
QuadraticInequalitiesContent	Quadratic inequalities are almost exactly the same as quadratic equations; the main difference is that quadratic inequalities have an inequality sign and quadratic equations have an equal sign. While quadratic equations' solutions represent the roots, or x-intercepts, of parabolas, quadratic inequalities' solutions represent the intervals between parabolas' roots on a graph. <br> There are several standard forms that quadratic inequalities can take. They are: <math>ax^2+bx+c>0</math> <math>ax^2+bx+c≥0</math> <math>ax^2+bx+c<0</math> <math>ax^2+bx+c≤0</math> <br> In these forms, <math>a</math>, <math>b</math> and <math>c</math> represent coefficients and <math>x</math> represents a variable that falls within the interval described by the inequality and, when substituted in place of <math>x</math>, renders a true mathematical statement (for example, <math>-2<0</math>). In order to find these intervals, we need to first understand where the parabola's roots are located. This can be determined using factorization or <a href="/en/terms-and-topics/solving-quadratic-equations-using-the-formula/">the quadratic formula</a>. Lastly, we need to decide in which of the intervals <math>x</math> correctly solves the inequality. <br> <img src="/images/quadraticInequalitiesGraph1.png" alt="circle graph"> <br> If the sign in the inequality is ≤ or ≥ then its roots are included in the interval and its parabola is drawn on a graph with a solid line. If the sign of the inequality is < or > then its roots are not included in the interval and its parabola is drawn on a graph with a dotted line. <br> When solving an inequality (much like when solving an equation), anything you do to one side of the inequality, you must also do to the other side of the inequality. <br> <a href="/en/solution/quadratic-inequalities/x%5E2%2B4x-5<4/">Learn how to solve quadratic inequalities</a>	Kvadratne nejednakosti su skoro potpuno iste kao i kvadratne jednačine; glavna razlika je u tome što kvadratne nejednakosti imaju predznak nejednakosti, a kvadratne jednačine imaju predznak jednakosti. Dok rešenja kvadratnih jednačina predstavljaju korene ili odsečke na x osi, parabole, rešenja kvadratnih nejednačina predstavljaju intervale između korena parabola na grafikonu. <br> Postoji nekoliko standardnih oblika koje kvadratne nejednakosti mogu poprimiti. To su: <math>ax^2+bx c>0</math> <math>ax^2+bx c≥0</math> <math>ax^2+bx c<0</math> <math>ax^2+bx c≤0</math> <br> U ovim oblicima, <math>a</math>, <math>b</math> i <math>c</math> predstavljaju koeficijente, a <math>x</math> predstavlja varijablu koja spada u interval opisanog nejednakošću i, kada je zamenjena umesto <math>x</math>, daje tačnu matematičku izjavu (na primer, <math>-2<0</math>). Da bismo pronašli ove intervale, prvo moramo razumeti gde se nalaze koreni parabole. To se može odrediti korišćenjem faktorizacije ili <a href="/en/terms-and-topics/solving-quadratic-equations-using-the-formula/">kvadratne formule</a>. Na kraju, moramo odlučiti u kom od intervala <math>x</math> ispravno rešava nejednakost. <br> <img src="/images/quadraticInequalitiesGraph1.png" alt="circle graph"> <br> Ako je predznak u nejednakosti ≤ ili ≥, tada su njeni koreni uključeni u interval i njena parabola je nacrtana na grafikonu punom linijom. Ako je predznak nejednakosti < ili >, tada njeni koreni nisu uključeni u interval i njena parabola je nacrtana na grafikonu isprekidanom linijom. <br> Prilikom rešavanja nejednačine (slično kao i kod rešavanja jednačine), sve što učinite na jednoj strani nejednakosti, morate učiniti i na drugoj strani nejednakosti. <br> <a href="/en/solution/quadratic-inequalities/x%5E2%2B4x-5<4/">Naučite kako rešiti kvadratne nejednakosti</a>
QuadraticInequalitiesSolver	Solving quadratic inequalities using the quadratic formula	Rešavanje kvadratnih nejednačina pomoću kvadratne formule
QuadraticInequalitiesSolver.plugin	solving quadratic inequalities using the quadratic formula	Rešavanje kvadratnih nejednačina pomoću kvadratne formule
RaisingtoaPower	Raising to a power	Stepenovanje
RaisingtoaPowerContent	Raising to a power, or exponentiation, is the process of multiplying a base value b by itself the number of times given by the exponent n in the term b^n. <br><br> So, for example, <math>3^4</math> is the same as <math>3 x 3 x 3 x 3</math>, which equals <math>81</math>. <br><br> This is spoken as “three to the fourth power” or “three to the fourth”. There are two exceptions to this: The power of two is generally called “squared” so <math>3^2</math> is “three squared”. The power of three is referred to as “cubed” so <math>3^3</math> is “three cubed”. <br><br> Exponents are especially useful when dealing with variables, such as <math>x^3</math>. There are a few rules in simplifying several variables raised to a power in one expression. <br><br> When two terms with the same base are multiplied, the exponents are added: <math>(b^n)(b^m) = b^(n+m)</math> <br><br> When raising a power to a power, the exponents are multiplied with each other: <math>(b^n)^m = b^(n*m)</math> In other words, if the entire expression <math>b^n</math> is raised to the power of <math>^m</math>, the new power of b is the product of n multiplied by m. <br><br> Any number to the power of zero equals 1, as long as the base value itself is not 0. <br><br> Enter your problem into Tiger’s calculator and the step-by-step solution will help you understand how to raise a number or an expression to a power.	Stepenovanje ili potenciranje je postupak množenja osnovne vrednosti b samim sobom onoliko puta koliko je eksponent n dat u članu b^n. <br><br> Tako je, na primer, <math>3^4</math> isto što i <math>3 x 3 x 3 x 3</math>, što je jednako <math>81</math>. <br><br> Ovo se govori kao „tri podignuto na četvrti eksponent“ ili „tri na četvrti”. Postoje dva izuzetka od toga: Eksponent dva se obično naziva „na kvadrat“, pa je <math>3^2</math> „na kvadrat“. Eksponent trojke naziva se „na treći“, tako da je <math>3^3</math> „na treći“. <br><br> Eksponenti su posebno korisni kada se radi o promenljivim, kao što je <math>x^3</math>. Postoji nekoliko pravila za pojednostavljivanje nekoliko promenljivih podignutih u stepen u jednom izrazu. <br><br> Kada se pomnože dva člana sa istom osnovom, dodaju se eksponenti: <math>(b^n)(b^m) = b^(n+m)</math> <br><br> Pri podizanju eksponenta u stepen, eksponenti se međusobno množe: <math>(b^n)^m = b^(n*m)</math> Drugim rečima, ako se celokupan izraz <math>b^n</math> podigne na stepen <math>^m</math>, nov eksponent b je proizvod n pomnožen sa m. <br><br> Bilo koji broj sa nulom jednak je 1, sve dok sama osnovna vrednost nije 0. <br><br> Unesi svoj problem u Tiger kalkulator i korak po korak rešenje će ti pomoći da razumeš kako podići broj ili izraz u stepen.
Range	Range	Raspon
ReducingFractionsToLowestTerms	Reducing fractions to lowest terms	Smanjenje razlomaka na najniže članove
ReducingFractionsToLowestTermsContent	A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. For example, if we examine the fraction <math>25/50</math>, we can reduce this fraction by dividing both the numerator and denominator by their common factor, 25. <math>25/25=1</math> and <math>50/25=2</math> then <math>25/50=1/2</math>. which is a fraction in its lowest terms.	Razlomak je najmanji član kada brojilac i nazivnik nemaju zajednički delilac osim 1. Na primer, ako ispitamo razlomak <math>25/50</math>, taj razlomak možemo smanjiti deljenjem brojioca i imenioca njihovim zajedničkim deliocem, 25. <math>25/25=1</math> i <math>50/25=2</math> tada <math>25/50=1/2</math>. što je razlomak skraćen na najniže članove.
RelatedLinks	Related links	Srodni linkovi
ResultsFound	Solution	Rešenje
ResultTypeMixedFractionForm	Mixed number form:	Mešoviti broj
ResultValue	{0}	{0}
RomanNumeralToInteger	Roman numeral to integer	Rimski broj u ceo broj
RomanNumeralToInteger.plugin	roman numeral to integer	rimski broj u ceo broj
RomanNumeralToIntegerStep1TextUnit1	Your input was cleaned into standard Roman numeral form: <math>{originalInput}</math> → <math>{normalizedRoman}</math>.	Ukloni razmake i pretvori rimski broj u velika slova: <math>{originalInput}</math> → <math>{normalizedRoman}</math>.
RomanNumeralToIntegerStep1Title1	Clean up the input	Normalizuj unos
RomanNumeralToIntegerStep2TextUnit1	Read left to right.<br>If a smaller symbol comes before a larger one, treat them as one subtractive pair (for example, IX = 9).<br>Otherwise, each symbol stands alone.<br><br>For this input we get:<br><br><math>{expandedValues}</math>	Proširi simbole/oduzimajuće parove u vrednosti: <br><br><math>{expandedValues}</math>
RomanNumeralToIntegerStep2Title1	Expand symbols	Proširi simbole
RomanNumeralToIntegerStep3TextUnit1	Now add the values:<br><math>{sumExpression}</math> = <math>{integerResult}</math>.<br><br>So <math>{normalizedRoman}</math> equals <math>{integerResult}</math>.	Saberi vrednosti: <math>{sumExpression}</math> = <math>{integerResult}</math>. Dakle <math>{normalizedRoman}</math> je jednako <math>{integerResult}</math>.

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English

Serbian 1305 characters edited Current translation Translated

Stepenovanje ili potenciranje je postupak množenja osnovne vrednosti b samim sobom onoliko puta koliko je eksponent n dat u članu b^n.
 
Tako je, na primer, <math>3^4</math> isto što i <math>3 x 3 x 3 x 3</math>, što je jednako <math>81</math>.
 
Ovo se govori kao „tri podignuto na četvrti eksponent“ ili „tri na četvrti”. Postoje dva izuzetka od toga: Eksponent dva se obično naziva „na kvadrat“, pa je <math>3^2</math> „na kvadrat“. Eksponent trojke naziva se „na treći“, tako da je <math>3^3</math> „na treći“.
 
Eksponenti su posebno korisni kada se radi o promenljivim, kao što je <math>x^3</math>. Postoji nekoliko pravila za pojednostavljivanje nekoliko promenljivih podignutih u stepen u jednom izrazu.
 
Kada se pomnože dva člana sa istom osnovom, dodaju se eksponenti:
<math>(b^n)(b^m) = b^(n+m)</math>
 
Pri podizanju eksponenta u stepen, eksponenti se međusobno množe:
<math>(b^n)^m = b^(n*m)</math>
Drugim rečima, ako se celokupan izraz
<math>b^n</math> podigne na stepen <math>^m</math>, nov eksponent b je proizvod n pomnožen sa m.
 
Bilo koji broj sa nulom jednak je 1, sve dok sama osnovna vrednost nije 0.
 
Unesi svoj problem u Tiger kalkulator i korak po korak rešenje će ti pomoći da razumeš kako podići broj ili izraz u stepen.

9 hours ago

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