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 R - Elementary Algebra Review - R.4 Polynomials - R.4 Exercise Set: 25

Answer

$\dfrac{9q^{8}}{4p^{6}}$

Work Step by Step

In order to simplify the expression, we distribute the -2 into the parenthesis. Using the laws of exponents, the given expression, $ \left( \dfrac{2p^3}{3q^4} \right)^{-2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2^{1(-2)}p^{3(-2)}}{3^{1(-2)}q^{4(-2)}} \\\\= \dfrac{2^{-2}p^{-6}}{3^{-2}q^{-8}} \\\\= \dfrac{3^{2}q^{8}}{2^{2}p^{6}} \\\\= \dfrac{9q^{8}}{4p^{6}} .\end{array}
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