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 - Page 522: 90



Work Step by Step

RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $(ab)^m = a^mb^m$ (iv) $(a^m)^n=a^{mn}$ Use the rules above to obtain: $=\left((2a)^{\frac{1}{8}}\right)^6 \\=(2a)^{\frac{1}{8} \cdot 6} \\=(2a)^{\frac{3}{4}} \\=\sqrt[4]{(2a)^3} \\=\sqrt[4]{2^3a^3} \\=\sqrt[4]{8a^3}$
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