Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.6 Rational Exponents - R.6 Exercises: 72

Answer

$\color{blue}{rs^{10}}$

Work Step by Step

RECALL: (1) $a^m \cdot a^n = a^{m+n}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $a^{1/n} = \sqrt[n]{a}$ (4) When $n$ is odd, $\sqrt[n]{a^n}=a$ (5) $a^{m/n} = \left(\sqrt[n]{a}\right)^m$ (6) $(ab)^m=a^mb^m$ (7) $(a^m)^n=a^{mn}$ Use rule (6) above to obtain: $=\dfrac{(r^{1/5})^{15}(s^{2/3})^{15}}{r^2}$ Use rule (7) above to obtain: $=\dfrac{r^{(1/5) \cdot 15}s^{(2/3) \cdot 15}}{r^2} \\=\dfrac{r^3y^{10}}{r^2}$ Use rule (2) above to obtain: $=r^{3-2}s^{10} \\=\color{blue}{rs^{10}}$
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