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: 73

Answer

$4.3^{1/2}$

Work Step by Step

Using the laws of exponents, the given expression, $ \dfrac{4.3^{-1/5}}{4.3^{-7/10}} ,$ simplifies to \begin{array}{l}\require{cancel} 4.3^{-\frac{1}{5}-\left( -\frac{7}{10} \right)} \\\\= 4.3^{-\frac{1}{5}+\frac{7}{10}} \\\\= 4.3^{-\frac{2}{10}+\frac{7}{10}} \\\\= 4.3^{\frac{5}{10}} \\\\= 4.3^{\frac{1}{2}} \\\\= 4.3^{1/2} .\end{array}
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