Intermediate Algebra (12th Edition)

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

Chapter 4 - Review Exercises: 17


$\dfrac{1}{96m^{7}} $

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{6m^{-4}}{m^{-9}} \right)^{-1}\left(\dfrac{m^{-2}}{16}\right) ,$ simplifies to \begin{array}{l}\require{cancel} \left( \dfrac{m^{-9}}{6m^{-4}} \right)^{1}\left(\dfrac{m^{-2}}{16}\right) \\\\= \dfrac{m^{-9}m^{-2}}{6(16)m^{-4}} \\\\= \dfrac{m^{-9+(-2)-(-4)}}{96} \\\\= \dfrac{m^{-9-2+4}}{96} \\\\= \dfrac{m^{-7}}{96} \\\\= \dfrac{1}{96m^{7}} .\end{array}
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