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: 81

Answer

$\dfrac{m^{1/3}}{n^{1/8}}$

Work Step by Step

Using the laws of exponents, the given expression, $ \left( m^{2/3}n^{-1/4} \right)^{1/2} ,$ simplifies to \begin{array}{l}\require{cancel} m^{\left( \frac{2}{3} \right) \left( \frac{1}{2} \right)}n^{\left( -\frac{1}{4} \right) \left( \frac{1}{2} \right)} \\\\= m^{\frac{2}{6}}n^{-\frac{1}{8}} \\\\= \dfrac{m^{\frac{1}{3}}}{n^{\frac{1}{8}}} \\\\= \dfrac{m^{1/3}}{n^{1/8}} .\end{array}
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