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: 91

Answer

$\sqrt[3]{x^2y}$

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) $(a^m)^n=a^{mn}$ (v) $\sqrt {a} \sqrt{b}= \sqrt{ab}$ Use the rules above to obtain: $=\left(x^6y^3\right)^{\frac{1}{9}} \\=(x^6)^{\frac{1}{9}}(y^3)^{\frac{1}{9}} \\=x^{6 \cdot \frac{1}{9}} \cdot y^{3\cdot\frac{1}{9}} \\=x^{\frac{2}{3}} \cdot y^{\frac{1}{3}} \\=\sqrt[3]{x^2} \cdot \sqrt[3]{y} \\=\sqrt[3]{x^2y}$
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