Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.1 Exponents and Their Properties - 4.1 Exercise Set: 83

Answer

$\dfrac{a^{12}}{16b^{20}}$

Work Step by Step

Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $ \left(\dfrac{a^3}{-2b^5}\right)^4 $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(a^3)^4}{(-2b^5)^4} .\end{array} Using $(a^x)^y=a^{xy}$, then the given expression, $ \dfrac{(a^3)^4}{(-2b^5)^4} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{a^{3(4)}}{(-2)^4b^{5(4)}} \\\\= \dfrac{a^{12}}{16b^{20}} .\end{array}
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