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: 72

Answer

$8^{9/11}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{8^{7/11}}{8^{-2/11}} ,$ simplifies to \begin{array}{l}\require{cancel} 8^{\frac{7}{11}-\left( -\frac{2}{11} \right)} \\\\= 8^{\frac{7}{11}+\frac{2}{11}} \\\\= 8^{\frac{9}{11}} \\\\= 8^{9/11} .\end{array}
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