Intermediate Algebra (12th Edition)

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

Chapter 4 - Review Exercises: 15

Answer

$\dfrac{r^{17}}{9}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{(3r)^2r^4}{r^{-2}r^{-3}}(9r^{-3})^{-2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{(3r)^2r^4(9r^{-3})^{-2}}{r^{-2}r^{-3}} \\\\= \dfrac{3^2r^2r^4(9)^{-2}r^{-3(-2)}}{r^{-2}r^{-3}} \\\\= \dfrac{3^2r^{2+4}(9)^{-2}r^{6}}{r^{-2+(-3)}} \\\\= \dfrac{3^2r^{6}r^{6}}{9^{2}r^{-5}} \\\\= \dfrac{9r^{6+6-(-5)}}{81} \\\\= \dfrac{r^{6+6+5}}{9} \\\\= \dfrac{r^{17}}{9} .\end{array}
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