Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Chapters R-4 - Cumulative Review Exercises: 30

Answer

$\dfrac{m^{6}}{8n^{9}}$

Work Step by Step

Use the laws of exponents to simplify the given expression, $ (2m^{-2}n^3)^{-3} .$ Using the extended Power Rule of the laws of exponents which states that $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2^{-3}m^{-2(-3)}n^{3(-3)} \\\\= 2^{-3}m^{6}n^{-9} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{m^{6}}{2^{3}n^{9}} \\\\= \dfrac{m^{6}}{8n^{9}} .\end{array}
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