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: 136

Answer

$\dfrac{m}{196}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{7m^{-2}}{m^{-3}} \right)^{-2} \cdot\dfrac{m^3}{4} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{m^{-3}}{7m^{-2}} \right)^{2} \cdot\dfrac{m^3}{4} \\\\= \dfrac{m^{-3(2)}}{7^2m^{-2(2)}} \cdot\dfrac{m^3}{4} \\\\= \dfrac{m^{-6}}{49m^{-4}} \cdot\dfrac{m^3}{4} \\\\= \dfrac{m^{-6+3}}{196m^{-4}} \\\\= \dfrac{m^{-3}}{196m^{-4}} \\\\= \dfrac{m^{-3-(-4)}}{196} \\\\= \dfrac{m^{-3+4}}{196} \\\\= \dfrac{m^{1}}{196} \\\\= \dfrac{m}{196} .\end{array}
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