Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises - Page 448: 52



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the definition of rational exponents to convert the given expression, $ \sqrt{5^{10}} ,$ to exponential form. $\bf{\text{Solution Details:}}$ 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} \sqrt[2]{5^{10}} \\\\= 5^{\frac{10}{2}} \\\\= 5^{5} \\\\= 3,125 .\end{array}
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