Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 93

Answer

$\sqrt[6]{32}$

Work Step by Step

RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ (iv) $a^m \cdot a^n = a^{m+n}$ Use rule (i) above to obtain: $=2^{\frac{1}{2}} \cdot 2^{\frac{1}{3}}$ Use rule (iv) above to obtain: $=2^{\frac{1}{2}+\frac{1}{3}} \\=2^{\frac{3}{6} + \frac{2}{6}} \\=2^{\frac{5}{6}}$ Use rule (iii) above, with m=5 and n=6, to obtain: $\\=\sqrt[6]{2^5} \\=\sqrt[6]{2(2)(2)(2)(2)} \\=\sqrt[6]{32}$
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