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: 82

Answer

$\dfrac{y^{1/10}}{x^{1/12}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( x^{-1/3}y^{2/5} \right)^{1/4} ,$ simplifies to \begin{array}{l}\require{cancel} x^{\left( -\frac{1}{3} \right) \left( \frac{1}{4} \right)}y^{\left( \frac{2}{5} \right) \left( \frac{1}{4} \right)} \\\\= x^{-\frac{1}{12}}y^{\frac{2}{20}} \\\\= x^{-\frac{1}{12}}y^{\frac{1}{10}} \\\\= \dfrac{y^{\frac{1}{10}}}{x^{\frac{1}{12}}} \\\\= \dfrac{y^{1/10}}{x^{1/12}} .\end{array}
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