Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 39

Answer

$\dfrac{x^{9}}{8y^{3}}$

Work Step by Step

Using laws of exponents, the given expression simplifies to \begin{align*} & \left( \dfrac{2x^{-3}}{y^{-1}} \right)^{-3} \\\\&= \dfrac{2^{-3}x^{-3(-3)}}{y^{-1(-3)}} \\\\&= \dfrac{2^{-3}x^{9}}{y^{3}} \\\\&= \dfrac{x^{9}}{2^{3}y^{3}} \\\\&= \dfrac{x^{9}}{8y^{3}} .\end{align*}
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