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: 135

Answer

$\dfrac{2k}{3}$

Work Step by Step

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