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: 70

Answer

$5^{3/8}$

Work Step by Step

Using the laws of exponents, the given expression, $ 5^{1/4}\cdot5^{1/8} ,$ simplifies to \begin{array}{l}\require{cancel} 5^{\frac{1}{4}+\frac{1}{8}} \\\\= 5^{\frac{2}{8}+\frac{1}{8}} \\\\= 5^{\frac{3}{8}} \\\\= 5^{3/8} .\end{array}
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