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: 66

Answer

$\color{blue}{25}$

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) $a^{m/n} = \left(\sqrt[n]{a}\right)^m$ Use rule (2) above to obtain: $=125^{7/3-5/3} \\=125^{2/3}$ Use rule (5) above to obtain: $=\left(\sqrt[3]{125}\right)^2 \\=\left(\sqrt[3]{5^3}\right)^2$ Use rule (4) above to obtain: $\\=5^2 \\=\color{blue}{25}$
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