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 - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 79



Work Step by Step

Using $\sqrt[n]{x^m}=(\sqrt[n]{x})^m=x^{m/n}$, the given expression, $ \sqrt[3]{a}\sqrt[6]{a} ,$ is equivalent to \begin{array}{l}\require{cancel} a^{\frac{1}{3}}\cdot a^{\frac{1}{6}} .\end{array} Using the least common denominator, 6, and the laws of exponents, the expression above simplifies to \begin{array}{l}\require{cancel} a^{\frac{2}{6}}\cdot a^{\frac{1}{6}} \\\\= a^{\frac{2}{6}+\frac{1}{6}} \\\\= a^{\frac{3}{6}} \\\\= a^{\frac{1}{2}} \\\\= \sqrt{a} .\end{array}
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