Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set: 66

Answer

$\sqrt[5]{\dfrac{512y^3z^3}{343x^3}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( \dfrac{7x}{8yz} \right)^{-3/5} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{8yz}{7x} \right)^{3/5} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $ \left( \dfrac{8yz}{7x} \right)^{3/5} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[5]{\left( \dfrac{8yz}{7x} \right)^{3}} \\\\= \sqrt[5]{\dfrac{8^3y^3z^3}{7^3x^3}} \\\\= \sqrt[5]{\dfrac{512y^3z^3}{343x^3}} .\end{array}
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