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 - Page 278: 143



Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{-3x^4y^6}{15x^{-6}y^7} \right)^{-3} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{(-3)^{-3}x^{4(-3)}y^{6(-3)}}{15^{-3}x^{-6(-3)}y^{7(-3)}} \\\\= \dfrac{(-3)^{-3}x^{-12}y^{-18}}{(-3)^{-3}(-5)^{-3}x^{18}y^{-21}} \\\\= \dfrac{\cancel{(-3)^{-3}}x^{-12-18}y^{-18-(-21)}}{\cancel{(-3)^{-3}}(-5)^{-3}} \\\\= \dfrac{x^{-12-18}y^{-18+21}}{(-5)^{-3}} \\\\= \dfrac{x^{-30}y^{3}}{(-5)^{-3}} \\\\= \dfrac{(-5)^{3}y^{3}}{x^{30}} \\\\= \dfrac{-125y^{3}}{x^{30}} \\\\= -\dfrac{125y^{3}}{x^{30}} .\end{array}
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