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: 85

Answer

$-\dfrac{125x^{21}y^3}{8z^{12}}$

Work Step by Step

Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $ \left(\dfrac{5x^7y}{-2z^4}\right)^3 $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(5x^7y)^3}{(-2z^4)^3} .\end{array} Using $(a^x)^y=a^{xy}$, then the given expression, $ \dfrac{(5x^7y)^3}{(-2z^4)^3} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{5^3x^{7(3)}y^3}{(-2)^3z^{4(3)}} \\\\= \dfrac{125x^{21}y^3}{-8z^{12}} \\\\= -\dfrac{125x^{21}y^3}{8z^{12}} .\end{array}
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