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: 82

Answer

$3a^4$

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) $(a^m)^n=a^{mn}$ Write $27$ as $3^3$ to obtain: $=\sqrt[3]{3^3a^{12}}$ Use rule (i) to obtain: $=(3^3a^{12})^{\frac{1}{3}}$ Use rule (iii) above to obtain: $=(3^3)^{\frac{1}{3}} \cdot (a^{12})^{\frac{1}{3}}$ Use rule (iv) above to obtain: $=3^{3\cdot\frac{1}{3}} \cdot a^{12 \cdot \frac{1}{3}} \\=3^1\cdot a^{4} \\=3a^4$
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