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: 86

Answer

$\dfrac{-64p^{15}}{27m^{6}n^{9}}$

Work Step by Step

Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $ \left(\dfrac{-4p^5}{3m^2n^3}\right)^3 $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(-4p^5)^3}{(3m^2n^3)^3} .\end{array} Using $(a^x)^y=a^{xy}$, then the given expression, $ \dfrac{(-4p^5)^3}{(3m^2n^3)^3} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(-4)^3p^{5(3)}}{3^3m^{2(3)}n^{3(3)}} \\\\= \dfrac{-64p^{15}}{27m^{6}n^{9}} .\end{array}
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