College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises: 64

Answer

$\sqrt[3]{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt[9]{5^3} ,$ use the definition of rational exponents. $\bf{\text{Solution Details:}}$ Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 5^{\frac{3}{9}} .\end{array} The expression above simplifies to \begin{array}{l}\require{cancel} 5^{\frac{1}{3}} \\\\= \sqrt[3]{5} .\end{array}
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