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: 82

Answer

$\dfrac{a^{20}}{b^{10}c^5}$

Work Step by Step

Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $ \left(\dfrac{a^4}{b^2c}\right)^5 $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(a^4)^5}{(b^2c)^5} .\end{array} Using $(a^x)^y=a^{xy}$, then the given expression, $ \dfrac{(a^4)^5}{(b^2c)^5} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{a^{4(5)}}{b^{2(5)}c^5} \\\\= \dfrac{a^{20}}{b^{10}c^5} .\end{array}
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