Variables Any lowercase letter may be used as a variable. 638+ Math Specialists 4.8/5 Quality score 85636+ Student Reviews Get Homework Help If there is a positive sign outside the bracket, then remove the bracket and write all the terms retaining their original signs. Exponents Calculator - Symbolab Use properties of rational exponents to simplify the expression Let's begin! Look at the above examples, and see whether and how we have used this property for the simplification of expressions. Need help? Negative Exponents in Fractions - Rule and Examples - Mechamath Simplifying Exponents. It can also perceive a color depth (gradations in colors) of up to 48 bits per frame, and can shoot the equivalent of 24 frames per second. This implies, 2ab + 4b (b2) - 4b (2a). How to Simplify an Expression with Parentheses & Exponents, Power of Powers: Simplifying Exponential Expressions, Graphing Systems of Equations | Overview, Process & Examples, Negative Exponents: Writing Powers of Fractions and Decimals. Step 1: Enter an exponential expression below which you want to simplify. 118 lessons Free simplify calculator - simplify algebraic expressions step-by-step. There will be times when working with expressions will be easier if you use rational exponents and times when it will be easier if you use radicals. There are many ways to improve your writing skills, but one of the most effective is to practice regularly. Use the properties of logarithms: If an expression contains logarithms, you can use the properties of logarithms to simplify it. Do not simplify further. Do not simplify further. Simple Rules of Exponents Let's look at some of the basic rules of exponents. The exponent calculator simplifies the given exponential expression using the laws of exponents. [latex]\begin{array}\text{ }x^{3}\cdot x^{4}\hfill&=\stackrel{\text{3 factors } \text{ 4 factors}}{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x} \\ \hfill& =\stackrel{7 \text{ factors}}{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x} \\ \hfill& =x^{7}\end{array}[/latex], [latex]{a}^{m}\cdot {a}^{n}={a}^{m+n}[/latex], [latex]{2}^{3}\cdot {2}^{4}={2}^{3+4}={2}^{7}[/latex]. By simplifying the expression, you can eliminate unnecessary terms and constants, making it easier to focus on the important parts of the equation and work through it step by step. Simplifying Expressions Calculator is a free online tool that displays the simplification of the given algebraic expression. To simplify an algebraic expression means to rewrite it in a simpler form, without changing its value. I feel like its a lifeline. Free simplify calculator - simplify algebraic expressions step-by-step. Next step - look at each part individually. In this expression, 6x and -3x are like terms, and -x2 and x2 are like terms. Quick-Start Guide Enter an equation in the box, then click "SIMPLIFY". Click the blue arrow to submit. We begin by using the associative and commutative properties of multiplication to regroup the factors. How to Simplify Expressions with Exponents - Study.com Multiplying Exponents | How to Multiply Exponents With Different Bases. [latex]{x}^{2}\cdot {x}^{5}\cdot {x}^{3}=\left({x}^{2}\cdot {x}^{5}\right)\cdot {x}^{3}=\left({x}^{2+5}\right)\cdot {x}^{3}={x}^{7}\cdot {x}^{3}={x}^{7+3}={x}^{10}[/latex], [latex]{x}^{2}\cdot {x}^{5}\cdot {x}^{3}={x}^{2+5+3}={x}^{10}[/latex], [latex]\begin{array}\text{ }\frac{y^{9}}{y^{5}}\hfill&=\frac{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}{y\cdot y\cdot y\cdot y\cdot y} \\ \hfill&=\frac{\cancel{y}\cdot\cancel{y}\cdot\cancel{y}\cdot\cancel{y}\cdot\cancel{y}\cdot y\cdot y\cdot y\cdot y}{\cancel{y}\cdot\cancel{y}\cdot\cancel{y}\cdot\cancel{y}\cdot\cancel{y}} \\ \hfill& =\frac{y\cdot y\cdot y\cdot y}{1} \\ \hfill& =y^{4}\end{array}[/latex], [latex]\frac{{a}^{m}}{{a}^{n}}={a}^{m-n}[/latex], [latex]\frac{{y}^{9}}{{y}^{5}}={y}^{9 - 5}={y}^{4}[/latex]. Quality is important in all aspects of life. To simplify an expression with fractions find a common denominator and then combine the numerators. How to simplify expressions with exponents calculator . For example, the expression 3x + 2y 4x + 5y can be simplified by combining like terms to get 3x 4x + 2y + 5y = -x + 7y. Simplify Calculator Simplify algebraic expressions step-by-step full pad Examples Related Symbolab blog posts Just like numbers have factors (23=6), expressions have factors ( ` . BYJU'S online simplifying. Let's try the best Simplify expressions . One way to think about math equations is to think of them as a puzzle. To simplify algebraic expressions, follow the steps given below: Step 1: Solve parentheses by adding/subtracting like terms inside and by multiplying the terms inside the brackets with the factor written outside. This calculator will try to simplify a polynomial as much as possible. See the steps to to. Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. Simplifying polynomials calculator - softmath 3 Ways to Solve Exponents - wikiHow Simplify is the same as reducing to lowest terms when we talk about fractions. As, in India, schools are closed so this is a very helpful app also for learning and answering for anyone, at first, when I took pictures with the camera it didn't always work, I didn't receive the answer I was looking for, because this app is so useful and easily accessable, my teacher doesn't allow it but they don't know that it shows you how to solve the problem which I think is awesome. Step 2: Click "Simplify" to get a simplified version of the entered expression. Yes. Overall, simplifying algebraic expressions is an important skill that can help you to save time, improve your understanding of math, and develop your problem-solving skills. Now, let us learn how to use the distributive property to simplify expressions with fractions. At first, it may appear that we cannot simplify a product of three factors. When simplifying math expressions, you can't simply proceed from left to right, multiplying, adding, subtracting, and so on as you go. The calculator allows with this computer algebra function of reducing an algebraic expression. Write answers with positive exponents. Algebra Topics: Simplifying Expressions - GCFGlobal.org BYJU'S online negative exponents calculator tool makes the calculation faster, and it displays the result in a fraction of seconds. For any real number [latex]a[/latex] and positive integers [latex]m[/latex] and [latex]n[/latex], the power rule of exponents states that. This website uses cookies to ensure you get the best experience on our website. Suppose an exponential expression is raised to some power. Simplify expressions with positive exponents calculator - This Simplify expressions with positive exponents calculator helps to fast and easily solve any math. Then the result is multiplied three times because the entire expression has an exponent of 3. . Step 2: Click the blue arrow to submit. It appears from the last two steps that we can use the power of a product rule as a power of a quotient rule. In this section, we review rules of exponents first and then apply them to calculations involving very large or small numbers. Choose "Simplify" from the topic selector and click to see the result in our Algebra Calculator! MathCelebrity.com's Simplify Radical Expressions Calculator - This calculator provides detailed . You can have more time for your hobbies by making small changes to your daily routine. Simplify, Simplify (a12b)12(ab12) ( ) One of the main benefits of simplifying expressions is that it can save you time and effort. In other words, [latex]{\left(pq\right)}^{3}={p}^{3}\cdot {q}^{3}[/latex]. The quotient rule of exponents allows us to simplify an expression that divides two numbers with the same base but different exponents. When simplifying expressions with exponents, rather than trying to work robotically from the rules, instead think about what the exponents mean. Simplify Math is a subject that often confuses students. What are the steps for simplifying expressions. . In this case, we would use the zero exponent rule of exponents to simplify the expression to 1. Let's look at an, Count the number of triangles in the given figure, Describe all solutions in parametric vector form, How to find inverse trig functions without calculator, How to find the central angle of a sector calculator, How to find the short diagonal of a rhombus, Math examples of graphing x and y coordinate equations. Solution: This expression only has the denominator with a negative exponent. For example, to express x2, enter x^2. simplify rational or radical expressions with our free step-by-step math calculator. y^9 divided by y^9 is y^(9-9). For any real number [latex]a[/latex] and natural numbers [latex]m[/latex] and [latex]n[/latex], the product rule of exponents states that. If there is a negative sign just outside parentheses, change the sign of all the terms written inside that bracket to simplify it. This time we have 5x^2y^9 / 15y^9x^4. Example 3: Daniel bought 5 pencils each costing $x, and Victoria bought 6 pencils each costing $x. Simplify Calculator - Solumaths Simplify the expression using the properties of rational exponents Simplify expressions with positive exponents calculator Ok. that was just a quick review. Solve - Properties of rational exponents calculator. Exponentiation is a mathematical operation, written as an, involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times. The power of a quotient of factors is the same as the quotient of the powers of the same factors. Example: Simplify the expression: 3/4x + y/2 (4x + 7). To simplify the power of a product of two exponential expressions, we can use the power of a product rule of exponents, which breaks up the power of a product of factors into the product of the powers of the factors. Math is the study of numbers, shapes, and patterns. I highly recommend you use this site! Simplify radical,rational expression with Step. This is our simplified answer with positive exponents. What are the steps for simplifying expressions Step 1: Identify the expression you need to simplify. If there is a negative sign outside the bracket, then remove the bracket and change the signs of all the terms written inside from + to -, and - to +. The cost of all 5 pencils = $5x. Check out all of our online calculators here! This is amazing, it helped me so often already! How to simplify algebraic expressions with exponents and variables Math problems can be determined by using a variety of methods. As a member, you'll also get unlimited access to over 88,000 Use our example, [latex]\frac{{h}^{3}}{{h}^{5}}[/latex]. The calculator above accepts negative bases, but does not compute imaginary numbers. Understanding of terms with exponents and exponent rules. Simplify expressions with positive exponents calculator - Math can be a challenging subject for many learners. Simplify x(6 - x) can be simplified as 6x - x2, and -x(3 - x) can be simplified as -3x + x2. Expand and simplify polynomials. We start at the beginning. Distributive property can be used to simplify the. Using b x b y = b x + y Simplify. This is true for any nonzero real number, or any variable representing a real number. Free simplify calculator - simplify algebraic expressions step-by-step. Example 1: Find the simplified form of the expression formed by the following statement: "Addition of k and 8 multiplied by the subtraction of k from 16". Know the order of operations. Here is an example: 2x^2+x(4x+3) Need more problem types? Write answers with positive exponents. Here are the basic steps to follow to simplify an algebraic expression: remove parentheses by multiplying factors use exponent rules to remove parentheses in terms with exponents combine like terms by adding coefficients combine the constants Let's work through an example. Simplify Algebraic Expressions Calculator - Neurochispas - Mechamath Factoring can help to make the expression more compact and easier to work with. Simplifying radical expressions calculator This calculator simplifies expressions that contain radicals. How to Simplify Expressions with Exponents - Study.com If you wish to solve the equation, use the Equation Solving Calculator. Simplifying Expressions with Distributive Property, Addition and subtraction of algebraic expressions. The sole exception is the expression [latex]{0}^{0}[/latex]. If so, then you will love the Simplify Calculator. In this blog post, we will be discussing How to simplify expressions with exponents calculator. By using the product rule of exponents, it can be written as 2ab + 4b3 - 8ab, which is equal to 4b3 - 6ab. 2 2 = 2 2 = 4 Square Root Calculator Calculate real and complex square roots (2nd order roots) of numbers or x. The basic rule for simplifying expressions is to combine like terms together and write unlike terms as it is. Type ^ for exponents like x^2 for x squared. Looking for support from expert professors? When we use rational exponents, we can apply the properties of exponents to simplify expressions. Here's the fun part, simplify. Now consider an example with real numbers. Indulging in rote learning, you are likely to forget concepts. In the denominator, I want the xs over each other and the ys over each other, so I write x^7y^3. Use the power rule to simplify each expression. Simplify the expression write answer with positive exponents calculator Math understanding that gets you Open up brackets, if any. Simplifying radical expressions with variables and exponents calculator Step 2: Click the blue arrow to submit and see the result! a. n times. Check these interesting articles related to the concept of simplifying expressions in math. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction. Algebra Basics - Simplifying - In Depth - math In other words, when multiplying exponential expressions with the same base, we write the result with the common base and add the exponents. To simplify your expression using the Simplify Calculator, type in your expression like 2 (5x+4)-3x. When one piece is missing, it can be difficult to see the whole picture. Check out our online math support services! Therefore, - k2 + 8k + 128 is the simplified form of the given expression. A really good app really I always used it for school (for a good benefit of course) and it really helps me understand math, although the camera sometimes takes a while to focus, I don't see this as a big issue. Expressions can be rewritten using exponents to be simplified visually and mathematically. To simplify expressions, we combine all the like terms and solve all the given brackets, if any, and then in the simplified expression, we will be only left with unlike terms that cannot be reduced further. Simplify radical,rational expression with Step The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. Simplify Rational Exponents - Minute Math Exponents are supported on variables using the ^ (caret) symbol. Estimating Square Roots | How Do You Find the Square Root of a Number? 16/8 is 2/1 times p^(1-3) times q^(2-4) times r^9. After this lesson you'll be able to simplify expressions with exponents. Core connections geometry textbook answers, Equation of a line parallel to another line through a point calculator, Find the volume of the hemisphere quizizz, Find the zeros of the following polynomial calculator, Finding the 5th term in a sequence calculator, How to find critical values of a function, Non homogeneous second order differential equation solver, Precalculus graphical numerical algebraic seventh edition. You can improve your academic performance by studying regularly and attending class. Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner. What our customers say Math app provides students with the tools they need to understand and solve their math problems, this app has been very helpful. We made the condition that [latex]m>n[/latex] so that the difference [latex]m-n[/latex] would never be zero or negative. If you're having problems memorizing these properties, I suggest using flash cards. Our final, simplified answer is y^5 / x^4. Divide one exponential expression by another with a larger exponent. Therefore, 3/4x + y/2 (4x + 7) = 3/4x + 2xy + 7y/2. Volume of a Cone: Examples | How Do You Find the Volume of a Cone? This simplified expression is equivalent to the original one, but it is written in a simpler and more compact form. By simplifying it further, we will get 3x, which will be the final answer. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. Some useful properties include: By using these properties, you can simplify complex expressions containing exponents. We know from our exponent properties that x^-4 is 1 / x^4 times y^5. Therefore, x (6 x) x (3 x) = 3x. And, Victoria bought 6 pencils each for $x, so the cost of 6 pencils = $6x. Since we have x^3 divided by x^7, we subtract their exponents. Our support team is available 24/7 to assist you. To find the product of powersMultiplication of two or more values in exponential form that have the same base-. Consider the example [latex]\frac{{y}^{9}}{{y}^{5}}[/latex]. Simplifying radical expressions calculator - mathportal.org 1 comment ( 7 votes) Upvote Downvote Flag more htom 2 years ago well what if something was like 1/2 to the power of 7 how would you solve that? Typing Exponents Type ^ for exponents like x^2 for "x squared". Kathryn teaches college math. Then it must be that ( 8 1 3) 3 = 8 3. If we equate the two answers, the result is [latex]{t}^{0}=1[/latex]. Simplify Our final answer is 2r^9 / (p^2 q^2). Then we simplify the terms containing exponents. For example, the expression 4x + 3y + 6x can be simplified by factoring out the common factor 2x to get x(4 + 6) + 3y = 10x + 3y. For any real number [latex]a[/latex] and natural numbers [latex]m[/latex] and [latex]n[/latex], such that [latex]m>n[/latex], the quotient rule of exponents states that. Enrolling in a course lets you earn progress by passing quizzes and exams. Free Exponents Calculator - Simplify exponential expressions using algebraic rules step-by-step. Simplify (m14n12)2(m2n3)12 By using the distributive property, the given expression can be written as 3/4x + y/2 (4x) + y/2 (7). We need to learn how to simplify expressions as it allows us to work more efficiently with algebraic expressions and ease out our calculations. This gives us y^8-3. Please ensure that your password is at least 8 characters and contains each of the following: You'll be able to enter math problems once our session is over. This tool is designed to take the frustration out of algebra by helping you to simplify and reduce your expressions to their simplest form. Use properties of rational exponents to simplify the expression calculator - Practice your math skills and learn step by step with our math solver. Exponent Base & Type | What is a Positive Exponent? All three are unlike terms, so it is the simplified form of the given expression. Can we simplify the result? The maximum possible number of bits of information used to film a one-hour (3,600-second) digital film is then an extremely large number. All rights reserved. It includes four examples. Absolutely amazing implementation Amazing features going way beyond a calculator Unbelievably user friendly, it has saved me many times. Simplifying radical expressions (addition) Google Classroom About Transcript A worked example of simplifying an expression that is a sum of several radicals. Simplify expressions using properties of exponents calculator Algebra Calculators Groups Cheat . A factor with a negative exponent becomes the same factor with a positive exponent if it is moved across the fraction barfrom numerator to denominator or vice versa. Expression Equation Inequality Contact us Simplify Factor Expand GCF LCM Our users: I purchased the Personal Algebra Tutor (PAT). The first step I like to do is put the like terms on top of each other. Examples Simplify Simplify Simplify We are asked to simplify using positive exponents: p^(-2) is the same as 1/p^2; q^(-2) is the same 1/q^2. Consider the product [latex]{x}^{3}\cdot {x}^{4}[/latex]. Flash cards are a fantastic and easy way to memorize topics, especially math properties. This calculator will solve your problems. Type ^ for exponents like x^2 for "x squared". simplify, solve for, expand, factor, rationalize. In the term , is the base and is the exponent. Sort by: Top Voted Questions Tips & Thanks This calculator will solve your problems. Exponent Calculator - Simplify Exponential Expression. (10^5=) The calculator should display the number 100,000, because that's equal to 10 5. If you need help, we're here for you 24/7. Simplifying Radical Expressions replace the square root sign ( ) with the letter r. show help examples Preview: Input Expression: Examples: r125 8/r2 (1+2r2)^2 Simplify the math operation ie., on multiplying the two large exponents, we will get the final output. Simplify Calculator - MathPapa Are you tired of struggling with complex algebraic expressions? Exponents Write each of the following quotients with a single base. Use the zero exponent and other rules to simplify each expression. 5.3: Simplify Rational Exponents - Mathematics LibreTexts Simplifying dividing algebraic expressions, solve 3x3 systems of linear equations with TI-84 calculator, solving parabola functions, Easiest way to Factor a third-degree polynomial. Analytical geometry of two and three dimensions in hindi, How do you subtract fractions step by step, How to find the volume of a prism with fractions, How to improve function of pituitary gland, Math problem solving worksheets for grade 1, What do vampires do on halloween math worksheet answers, What is the order of differential equation given by dy/dx+4y=sinx. Simplify mathematical expressions involving addition, subtraction, multiplication, division, and exponents Simplify Expressions Using the Order of Operations We've introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations. 986+ Experts. There are a lot of letters and numbers here, but don't let them trick you. First, we open the brackets, if any. expression calculator synthetic division calculator program multiply expressions with fractional exponents. Basic knowledge of algebraic expressions is required. Try refreshing the page, or contact customer support. Answer Comment ( 3 votes) Upvote Downvote Flag more Also, instead of qualifying variables as nonzero each time, we will simplify matters and assume from here on that all variables represent nonzero real numbers. And, y/2 7/1 = 7y/2. In this example, we simplify (2x)+48+3 (2x)+8. Use this, i was struggling with simplifying but this calculator has everything needed, this app was amazing and the best responses and the best Solutions I would refer this to everyone . [latex]\frac{{t}^{8}}{{t}^{8}}={t}^{8 - 8}={t}^{0}[/latex]. [latex]{\left({e}^{-2}{f}^{2}\right)}^{7}=\frac{{f}^{14}}{{e}^{14}}[/latex], [latex]\begin{array}{ccc}\hfill {\left({e}^{-2}{f}^{2}\right)}^{7}& =& {\left(\frac{{f}^{2}}{{e}^{2}}\right)}^{7}\hfill \\ & =& \frac{{f}^{14}}{{e}^{14}}\hfill \end{array}[/latex], [latex]\begin{array}{ccc}\hfill {\left({e}^{-2}{f}^{2}\right)}^{7}& =& {\left(\frac{{f}^{2}}{{e}^{2}}\right)}^{7}\hfill \\ & =& \frac{{\left({f}^{2}\right)}^{7}}{{\left({e}^{2}\right)}^{7}}\hfill \\ & =& \frac{{f}^{2\cdot 7}}{{e}^{2\cdot 7}}\hfill \\ & =& \frac{{f}^{14}}{{e}^{14}}\hfill \end{array}[/latex], [latex]{\left(\frac{a}{b}\right)}^{n}=\frac{{a}^{n}}{{b}^{n}}[/latex], CC licensed content, Specific attribution, http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2, http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface, [latex]\left(3a\right)^{7}\cdot\left(3a\right)^{10} [/latex], [latex]\left(\left(3a\right)^{7}\right)^{10} [/latex], [latex]\left(3a\right)^{7\cdot10} [/latex], [latex]{\left(a\cdot b\right)}^{n}={a}^{n}\cdot {b}^{n}[/latex], [latex]\left(-3\right)^{5}\cdot \left(-3\right)[/latex], [latex]{x}^{2}\cdot {x}^{5}\cdot {x}^{3}[/latex], [latex]{t}^{5}\cdot {t}^{3}={t}^{5+3}={t}^{8}[/latex], [latex]{\left(-3\right)}^{5}\cdot \left(-3\right)={\left(-3\right)}^{5}\cdot {\left(-3\right)}^{1}={\left(-3\right)}^{5+1}={\left(-3\right)}^{6}[/latex], [latex]{\left(\frac{2}{y}\right)}^{4}\cdot \left(\frac{2}{y}\right)[/latex], [latex]{t}^{3}\cdot {t}^{6}\cdot {t}^{5}[/latex], [latex]{\left(\frac{2}{y}\right)}^{5}[/latex], [latex]\frac{{\left(-2\right)}^{14}}{{\left(-2\right)}^{9}}[/latex], [latex]\frac{{\left(z\sqrt{2}\right)}^{5}}{z\sqrt{2}}[/latex], [latex]\frac{{\left(-2\right)}^{14}}{{\left(-2\right)}^{9}}={\left(-2\right)}^{14 - 9}={\left(-2\right)}^{5}[/latex], [latex]\frac{{t}^{23}}{{t}^{15}}={t}^{23 - 15}={t}^{8}[/latex], [latex]\frac{{\left(z\sqrt{2}\right)}^{5}}{z\sqrt{2}}={\left(z\sqrt{2}\right)}^{5 - 1}={\left(z\sqrt{2}\right)}^{4}[/latex], [latex]\frac{{\left(-3\right)}^{6}}{-3}[/latex], [latex]\frac{{\left(e{f}^{2}\right)}^{5}}{{\left(e{f}^{2}\right)}^{3}}[/latex], [latex]{\left(e{f}^{2}\right)}^{2}[/latex], [latex]{\left({x}^{2}\right)}^{7}[/latex], [latex]{\left({\left(2t\right)}^{5}\right)}^{3}[/latex], [latex]{\left({\left(-3\right)}^{5}\right)}^{11}[/latex], [latex]{\left({x}^{2}\right)}^{7}={x}^{2\cdot 7}={x}^{14}[/latex], [latex]{\left({\left(2t\right)}^{5}\right)}^{3}={\left(2t\right)}^{5\cdot 3}={\left(2t\right)}^{15}[/latex], [latex]{\left({\left(-3\right)}^{5}\right)}^{11}={\left(-3\right)}^{5\cdot 11}={\left(-3\right)}^{55}[/latex], [latex]{\left({\left(3y\right)}^{8}\right)}^{3}[/latex], [latex]{\left({t}^{5}\right)}^{7}[/latex], [latex]{\left({\left(-g\right)}^{4}\right)}^{4}[/latex], [latex]\frac{{\left({j}^{2}k\right)}^{4}}{\left({j}^{2}k\right)\cdot {\left({j}^{2}k\right)}^{3}}[/latex], [latex]\frac{5{\left(r{s}^{2}\right)}^{2}}{{\left(r{s}^{2}\right)}^{2}}[/latex], [latex]\begin{array}\text{ }\frac{c^{3}}{c^{3}} \hfill& =c^{3-3} \\ \hfill& =c^{0} \\ \hfill& =1\end{array}[/latex], [latex]\begin{array}{ccc}\hfill \frac{-3{x}^{5}}{{x}^{5}}& =& -3\cdot \frac{{x}^{5}}{{x}^{5}}\hfill \\ & =& -3\cdot {x}^{5 - 5}\hfill \\ & =& -3\cdot {x}^{0}\hfill \\ & =& -3\cdot 1\hfill \\ & =& -3\hfill \end{array}[/latex], [latex]\begin{array}{cccc}\hfill \frac{{\left({j}^{2}k\right)}^{4}}{\left({j}^{2}k\right)\cdot {\left({j}^{2}k\right)}^{3}}& =& \frac{{\left({j}^{2}k\right)}^{4}}{{\left({j}^{2}k\right)}^{1+3}}\hfill & \text{Use the product rule in the denominator}.\hfill \\ & =& \frac{{\left({j}^{2}k\right)}^{4}}{{\left({j}^{2}k\right)}^{4}}\hfill & \text{Simplify}.\hfill \\ & =& {\left({j}^{2}k\right)}^{4 - 4}\hfill & \text{Use the quotient rule}.\hfill \\ & =& {\left({j}^{2}k\right)}^{0}\hfill & \text{Simplify}.\hfill \\ & =& 1& \end{array}[/latex], [latex]\begin{array}{cccc}\hfill \frac{5{\left(r{s}^{2}\right)}^{2}}{{\left(r{s}^{2}\right)}^{2}}& =& 5{\left(r{s}^{2}\right)}^{2 - 2}\hfill & \text{Use the quotient rule}.\hfill \\ & =& 5{\left(r{s}^{2}\right)}^{0}\hfill & \text{Simplify}.\hfill \\ & =& 5\cdot 1\hfill & \text{Use the zero exponent rule}.\hfill \\ & =& 5\hfill & \text{Simplify}.\hfill \end{array}[/latex], [latex]\frac{{\left(d{e}^{2}\right)}^{11}}{2{\left(d{e}^{2}\right)}^{11}}[/latex], [latex]\frac{{w}^{4}\cdot {w}^{2}}{{w}^{6}}[/latex], [latex]\frac{{t}^{3}\cdot {t}^{4}}{{t}^{2}\cdot {t}^{5}}[/latex], [latex]\frac{{\theta }^{3}}{{\theta }^{10}}[/latex], [latex]\frac{{z}^{2}\cdot z}{{z}^{4}}[/latex], [latex]\frac{{\left(-5{t}^{3}\right)}^{4}}{{\left(-5{t}^{3}\right)}^{8}}[/latex], [latex]\frac{{\theta }^{3}}{{\theta }^{10}}={\theta }^{3 - 10}={\theta }^{-7}=\frac{1}{{\theta }^{7}}[/latex], [latex]\frac{{z}^{2}\cdot z}{{z}^{4}}=\frac{{z}^{2+1}}{{z}^{4}}=\frac{{z}^{3}}{{z}^{4}}={z}^{3 - 4}={z}^{-1}=\frac{1}{z}[/latex], [latex]\frac{{\left(-5{t}^{3}\right)}^{4}}{{\left(-5{t}^{3}\right)}^{8}}={\left(-5{t}^{3}\right)}^{4 - 8}={\left(-5{t}^{3}\right)}^{-4}=\frac{1}{{\left(-5{t}^{3}\right)}^{4}}[/latex], [latex]\frac{{\left(-3t\right)}^{2}}{{\left(-3t\right)}^{8}}[/latex], [latex]\frac{{f}^{47}}{{f}^{49}\cdot f}[/latex], [latex]\frac{1}{{\left(-3t\right)}^{6}}[/latex], [latex]{\left(-x\right)}^{5}\cdot {\left(-x\right)}^{-5}[/latex], [latex]\frac{-7z}{{\left(-7z\right)}^{5}}[/latex], [latex]{b}^{2}\cdot {b}^{-8}={b}^{2 - 8}={b}^{-6}=\frac{1}{{b}^{6}}[/latex], [latex]{\left(-x\right)}^{5}\cdot {\left(-x\right)}^{-5}={\left(-x\right)}^{5 - 5}={\left(-x\right)}^{0}=1[/latex], [latex]\frac{-7z}{{\left(-7z\right)}^{5}}=\frac{{\left(-7z\right)}^{1}}{{\left(-7z\right)}^{5}}={\left(-7z\right)}^{1 - 5}={\left(-7z\right)}^{-4}=\frac{1}{{\left(-7z\right)}^{4}}[/latex], [latex]\frac{{25}^{12}}{{25}^{13}}[/latex], [latex]{t}^{-5}=\frac{1}{{t}^{5}}[/latex], [latex]{\left(a{b}^{2}\right)}^{3}[/latex], [latex]{\left(-2{w}^{3}\right)}^{3}[/latex], [latex]\frac{1}{{\left(-7z\right)}^{4}}[/latex], [latex]{\left({e}^{-2}{f}^{2}\right)}^{7}[/latex], [latex]{\left(a{b}^{2}\right)}^{3}={\left(a\right)}^{3}\cdot {\left({b}^{2}\right)}^{3}={a}^{1\cdot 3}\cdot {b}^{2\cdot 3}={a}^{3}{b}^{6}[/latex], [latex]2{t}^{15}={\left(2\right)}^{15}\cdot {\left(t\right)}^{15}={2}^{15}{t}^{15}=32,768{t}^{15}[/latex], [latex]{\left(-2{w}^{3}\right)}^{3}={\left(-2\right)}^{3}\cdot {\left({w}^{3}\right)}^{3}=-8\cdot {w}^{3\cdot 3}=-8{w}^{9}[/latex], [latex]\frac{1}{{\left(-7z\right)}^{4}}=\frac{1}{{\left(-7\right)}^{4}\cdot {\left(z\right)}^{4}}=\frac{1}{2,401{z}^{4}}[/latex], [latex]{\left({e}^{-2}{f}^{2}\right)}^{7}={\left({e}^{-2}\right)}^{7}\cdot {\left({f}^{2}\right)}^{7}={e}^{-2\cdot 7}\cdot {f}^{2\cdot 7}={e}^{-14}{f}^{14}=\frac{{f}^{14}}{{e}^{14}}[/latex], [latex]{\left({g}^{2}{h}^{3}\right)}^{5}[/latex], [latex]{\left(-3{y}^{5}\right)}^{3}[/latex], [latex]\frac{1}{{\left({a}^{6}{b}^{7}\right)}^{3}}[/latex], [latex]{\left({r}^{3}{s}^{-2}\right)}^{4}[/latex], [latex]\frac{1}{{a}^{18}{b}^{21}}[/latex], [latex]{\left(\frac{4}{{z}^{11}}\right)}^{3}[/latex], [latex]{\left(\frac{p}{{q}^{3}}\right)}^{6}[/latex], [latex]{\left(\frac{-1}{{t}^{2}}\right)}^{27}[/latex], [latex]{\left({j}^{3}{k}^{-2}\right)}^{4}[/latex], [latex]{\left({m}^{-2}{n}^{-2}\right)}^{3}[/latex], [latex]{\left(\frac{4}{{z}^{11}}\right)}^{3}=\frac{{\left(4\right)}^{3}}{{\left({z}^{11}\right)}^{3}}=\frac{64}{{z}^{11\cdot 3}}=\frac{64}{{z}^{33}}[/latex], [latex]{\left(\frac{p}{{q}^{3}}\right)}^{6}=\frac{{\left(p\right)}^{6}}{{\left({q}^{3}\right)}^{6}}=\frac{{p}^{1\cdot 6}}{{q}^{3\cdot 6}}=\frac{{p}^{6}}{{q}^{18}}[/latex], [latex]{\\left(\frac{-1}{{t}^{2}}\\right)}^{27}=\frac{{\\left(-1\\right)}^{27}}{{\\left({t}^{2}\\right)}^{27}}=\frac{-1}{{t}^{2\cdot 27}}=\frac{-1}{{t}^{54}}=-\frac{1}{{t}^{54}}[/latex], [latex]{\left({j}^{3}{k}^{-2}\right)}^{4}={\left(\frac{{j}^{3}}{{k}^{2}}\right)}^{4}=\frac{{\left({j}^{3}\right)}^{4}}{{\left({k}^{2}\right)}^{4}}=\frac{{j}^{3\cdot 4}}{{k}^{2\cdot 4}}=\frac{{j}^{12}}{{k}^{8}}[/latex], [latex]{\left({m}^{-2}{n}^{-2}\right)}^{3}={\left(\frac{1}{{m}^{2}{n}^{2}}\right)}^{3}=\frac{{\left(1\right)}^{3}}{{\left({m}^{2}{n}^{2}\right)}^{3}}=\frac{1}{{\left({m}^{2}\right)}^{3}{\left({n}^{2}\right)}^{3}}=\frac{1}{{m}^{2\cdot 3}\cdot {n}^{2\cdot 3}}=\frac{1}{{m}^{6}{n}^{6}}[/latex], [latex]{\left(\frac{{b}^{5}}{c}\right)}^{3}[/latex], [latex]{\left(\frac{5}{{u}^{8}}\right)}^{4}[/latex], [latex]{\left(\frac{-1}{{w}^{3}}\right)}^{35}[/latex], [latex]{\left({p}^{-4}{q}^{3}\right)}^{8}[/latex], [latex]{\left({c}^{-5}{d}^{-3}\right)}^{4}[/latex], [latex]\frac{1}{{c}^{20}{d}^{12}}[/latex], [latex]{\left(6{m}^{2}{n}^{-1}\right)}^{3}[/latex], [latex]{17}^{5}\cdot {17}^{-4}\cdot {17}^{-3}[/latex], [latex]{\left(\frac{{u}^{-1}v}{{v}^{-1}}\right)}^{2}[/latex], [latex]\left(-2{a}^{3}{b}^{-1}\right)\left(5{a}^{-2}{b}^{2}\right)[/latex], [latex]{\left({x}^{2}\sqrt{2}\right)}^{4}{\left({x}^{2}\sqrt{2}\right)}^{-4}[/latex], [latex]\frac{{\left(3{w}^{2}\right)}^{5}}{{\left(6{w}^{-2}\right)}^{2}}[/latex], [latex]\begin{array}{cccc}\hfill {\left(6{m}^{2}{n}^{-1}\right)}^{3}& =& {\left(6\right)}^{3}{\left({m}^{2}\right)}^{3}{\left({n}^{-1}\right)}^{3}\hfill & \text{The power of a product rule}\hfill \\ & =& {6}^{3}{m}^{2\cdot 3}{n}^{-1\cdot 3}\hfill & \text{The power rule}\hfill \\ & =& \text{ }216{m}^{6}{n}^{-3}\hfill & \text{Simplify}.\hfill \\ & =& \frac{216{m}^{6}}{{n}^{3}}\hfill & \text{The negative exponent rule}\hfill \end{array}[/latex], [latex]\begin{array}{cccc}\hfill {17}^{5}\cdot {17}^{-4}\cdot {17}^{-3}& =& {17}^{5 - 4-3}\hfill & \text{The product rule}\hfill \\ & =& {17}^{-2}\hfill & \text{Simplify}.\hfill \\ & =& \frac{1}{{17}^{2}}\text{ or }\frac{1}{289}\hfill & \text{The negative exponent rule}\hfill \end{array}[/latex], [latex]\begin{array}{cccc}\hfill {\left(\frac{{u}^{-1}v}{{v}^{-1}}\right)}^{2}& =& \frac{{\left({u}^{-1}v\right)}^{2}}{{\left({v}^{-1}\right)}^{2}}\hfill & \text{The power of a quotient rule}\hfill \\ & =& \frac{{u}^{-2}{v}^{2}}{{v}^{-2}}\hfill & \text{The power of a product rule}\hfill \\ & =& {u}^{-2}{v}^{2-\left(-2\right)}& \text{The quotient rule}\hfill \\ & =& {u}^{-2}{v}^{4}\hfill & \text{Simplify}.\hfill \\ & =& \frac{{v}^{4}}{{u}^{2}}\hfill & \text{The negative exponent rule}\hfill \end{array}[/latex], [latex]\begin{array}{cccc}\hfill \left(-2{a}^{3}{b}^{-1}\right)\left(5{a}^{-2}{b}^{2}\right)& =& -2\cdot 5\cdot {a}^{3}\cdot {a}^{-2}\cdot {b}^{-1}\cdot {b}^{2}\hfill & \text{Commutative and associative laws of multiplication}\hfill \\ & =& -10\cdot {a}^{3 - 2}\cdot {b}^{-1+2}\hfill & \text{The product rule}\hfill \\ & =& -10ab\hfill & \text{Simplify}.\hfill \end{array}[/latex], [latex]\begin{array}{cccc}\hfill {\left({x}^{2}\sqrt{2}\right)}^{4}{\left({x}^{2}\sqrt{2}\right)}^{-4}& =& {\left({x}^{2}\sqrt{2}\right)}^{4 - 4}\hfill & \text{The product rule}\hfill \\ & =& \text{ }{\left({x}^{2}\sqrt{2}\right)}^{0}\hfill & \text{Simplify}.\hfill \\ & =& 1\hfill & \text{The zero exponent rule}\hfill \end{array}[/latex], [latex]\begin{array}{cccc}\hfill \frac{{\left(3{w}^{2}\right)}^{5}}{{\left(6{w}^{-2}\right)}^{2}}& =& \frac{{\left(3\right)}^{5}\cdot {\left({w}^{2}\right)}^{5}}{{\left(6\right)}^{2}\cdot {\left({w}^{-2}\right)}^{2}}\hfill & \text{The power of a product rule}\hfill \\ & =& \frac{{3}^{5}{w}^{2\cdot 5}}{{6}^{2}{w}^{-2\cdot 2}}\hfill & \text{The power rule}\hfill \\ & =& \frac{243{w}^{10}}{36{w}^{-4}}\hfill & \text{Simplify}.\hfill \\ & =& \frac{27{w}^{10-\left(-4\right)}}{4}\hfill & \text{The quotient rule and reduce fraction}\hfill \\ & =& \frac{27{w}^{14}}{4}\hfill & \text{Simplify}.\hfill \end{array}[/latex], [latex]{\left(2u{v}^{-2}\right)}^{-3}[/latex], [latex]{x}^{8}\cdot {x}^{-12}\cdot x[/latex], [latex]{\left(\frac{{e}^{2}{f}^{-3}}{{f}^{-1}}\right)}^{2}[/latex], [latex]\left(9{r}^{-5}{s}^{3}\right)\left(3{r}^{6}{s}^{-4}\right)[/latex], [latex]{\left(\frac{4}{9}t{w}^{-2}\right)}^{-3}{\left(\frac{4}{9}t{w}^{-2}\right)}^{3}[/latex], [latex]\frac{{\left(2{h}^{2}k\right)}^{4}}{{\left(7{h}^{-1}{k}^{2}\right)}^{2}}[/latex].
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how to simplify expressions with exponents calculator