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: 146

Answer

$\dfrac{36}{r^{14}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{(3r^2)^2r^{-5}}{r^{-2}r^{3}}(2r^{-6})^{2} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{3^2r^4r^{-5}(2^2r^{-6(2)})}{r^{-2}r^{3}} \\\\= \dfrac{9r^4r^{-5}(4r^{-12})}{r^{-2}r^{3}} \\\\= 36r^{4+(-5)+(-12)-(-2)-3} \\\\= 36r^{4-5-12+2-3} \\\\= 36r^{-14} \\\\= \dfrac{36}{r^{14}} .\end{array}
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