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: 134

Answer

$\dfrac{s^{2}}{81r^{4}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{(3rs)^{-2}}{3^2r^2s^{-4}} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{3^{-2}r^{-2}s^{-2}}{3^2r^2s^{-4}} \\\\= 3^{-2-2}r^{-2-2}s^{-2-(-4)} \\\\= 3^{-2-2}r^{-2-2}s^{-2+4} \\\\= 3^{-4}r^{-4}s^{2} \\\\= \dfrac{s^{2}}{3^{4}r^{4}} \\\\= \dfrac{s^{2}}{81r^{4}} .\end{array}
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