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: 74

Answer

$\dfrac{x^{\frac{1}{12}}}{y^{\frac{2}{15}}}$

Work Step by Step

RECALL: (1) $(a^m)^n=a^{mn}$ (2) $(ab)^m = a^mb^m$ (3) $a^{\frac{1}{n}}= \sqrt[n]{a}$ (4) $a^{-m} = \dfrac{1}{a^m}$ Use rule (2) above to obtain: $=(x^{\frac{1}{4}})^{\frac{1}{3}}(y^{-\frac{2}{5}})^{\frac{1}{3}}$ Use rule (1) above to obtain: $=x^{\frac{1}{4}\cdot \frac{1}{3}}y^{-\frac{2}{5}(\frac{1}{3})} \\=x^{\frac{1}{12}}y^{-\frac{2}{15}}$ Use rule (4) above to obtain: $=x^{\frac{1}{12}} \cdot \dfrac{1}{y^{\frac{2}{15}}} \\=\dfrac{x^{\frac{1}{12}}}{y^{\frac{2}{15}}}$
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