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 ( ` . However, when simplifying expressions containing exponents, don't feel like you must work only with, or straight from, these rules. flashcard sets. . It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. 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? To use the Simplify Calculator, simply enter your expression into the input field and press the "Calculate" button. expression calculator synthetic division calculator program multiply expressions with fractional exponents. By simplifying it further, we will get 3x, which will be the final answer. Use the product and quotient rules and the new definitions to simplify each expression. Do not simplify further. The quotient rule of exponents allows us to simplify an expression that divides two numbers with the same base but different exponents. . How to Define a Zero and Negative Exponent, How to Simplify Expressions with Exponents, Simplifying Expressions with Rational Exponents, How to Graph Cubics, Quartics, Quintics and Beyond, How to Add, Subtract and Multiply Polynomials, How to Divide Polynomials with Long Division, How to Use Synthetic Division to Divide Polynomials, Remainder Theorem & Factor Theorem: Definition & Examples, Dividing Polynomials with Long and Synthetic Division: Practice Problems, Practice Problem Set for Exponents and Polynomials, Introduction to Statistics: Tutoring Solution, Study.com ACT® Test Prep: Help and Review, Prentice Hall Algebra 2: Online Textbook Help, College Preparatory Mathematics: Help and Review, McDougal Littell Pre-Algebra: Online Textbook Help, High School Algebra II: Homeschool Curriculum, How to Write a Numerical Expression? The exponent calculator simplifies the given exponential expression using the laws of exponents. Step 1: Enter the algebraic expression in the corresponding input box. When simplifying expressions with exponents, rather than trying to work robotically from the rules, instead think about what the exponents mean. Factor the expression: Factoring an expression involves identifying common factors among the terms and pulling them out of the expression using parentheses. For example, 1/2 (x + 4) can be simplified as x/2 + 2. 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. It appears from the last two steps that we can use the power of a product rule as a power of a quotient rule. MathCelebrity.com's Simplify Radical Expressions Calculator - This calculator provides detailed . Step 1, how do i find my safe credit union account number, how to write a number in expanded form in two ways, simplify expressions with rational exponents calculator. For example, lets look at the following example. Solve - Properties of rational exponents calculator. Then it must be that ( 8 1 3) 3 = 8 3. It does not intend to find the value of an unknown quantity. Step 1: Enter the expression you want to simplify into the editor. We need to learn how to simplify expressions as it allows us to work more efficiently with algebraic expressions and ease out our calculations. For any real numbers [latex]a[/latex] and [latex]b[/latex], where [latex]b\neq0[/latex], and any integer [latex]n[/latex], the power of a quotient rule of exponents states that. Quick-Start Guide Enter an equation in the box, then click "SIMPLIFY". Well, 5 is positive, so we don't need to change it. Ok. that was just a quick review. Whether you are a student working on math assignments or a professional dealing with equations as part of your job, learning to simplify expressions is a valuable investment in your mathematical education and career. Let's assume we are now not limited to whole numbers. Are you tired of struggling with complex algebraic expressions? Simple Rules of Exponents Let's look at some of the basic rules of exponents. Simplifying radical expressions (addition) Google Classroom About Transcript A worked example of simplifying an expression that is a sum of several radicals. Free Exponents Calculator - Simplify exponential expressions using algebraic rules step-by-step. Therefore, 4(2a + 3a + 4) + 6b is simplified as 20a + 6b + 16. To unlock this lesson you must be a Study.com Member. I highly recommend you use this site! Example of Dividing Monomials When you divide monomial expressions, subtract the exponents of like bases. . We follow the same PEMDAS rule to simplify algebraic expressions as we do for simple arithmetic expressions. All three are unlike terms, so it is the simplified form of the given expression. 2 2 = 2 2 = 4 Square Root Calculator Calculate real and complex square roots (2nd order roots) of numbers or x. Homework is a necessary part of school that helps students review and practice what they have learned in class. Simplifying mathematical expressions implies rewriting the same algebraic statement compactly with no like terms. [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].
how to simplify expressions with exponents calculatorLeave a Reply