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: 81

Answer

$2a^2$

Work Step by Step

RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $(ab)^m = a^mb^m$ Use rule (i) above to obtain: $=(8a^6)^{\frac{1}{3}}$ Use rule (iii) above to obtain: $=8^{\frac{1}{3}}(a^6)^{\frac{1}{3}} \\=(2^3)^{\frac{1}{3}}a^{6\cdot \frac{1}{3}} \\=2^{3 \cdot \frac{1}{3}} a^2 \\=2^1a^2 \\=2a^2$
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