Intermediate Algebra (12th Edition)

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

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises: 140

Answer

$\dfrac{m^{4}}{27}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{3^{-1}m^4(m^2)^{-1}}{3^2m^{-2}} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{3^{-1}m^4m^{2(-1)}}{3^2m^{-2}} \\\\= \dfrac{3^{-1}m^4m^{-2}}{3^2m^{-2}} \\\\= 3^{-1-2}m^{4+(-2)-(-2)} \\\\= 3^{-3}m^{4-2+2} \\\\= \dfrac{m^{4}}{3^{3}} \\\\= \dfrac{m^{4}}{27} .\end{array}
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