Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 425: 91

Answer

$\sqrt[]{a}$

Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then, \begin{array}{l} \dfrac{\sqrt[3]{a^2}}{\sqrt[6]{a}} \\\\= \dfrac{a^{2/3}}{a^{1/6}} \\\\= a^{\frac{2}{3}-\frac{1}{6}} \\\\= a^{\frac{4}{6}-\frac{1}{6}} \\\\= a^{\frac{3}{6}} \\\\= a^{\frac{1}{2}} \\\\= \sqrt[]{a} .\end{array}
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