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: 77

Answer

$\color{blue}{p^{11/6}}$

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) $(a^m)^n=a^{mn}$ (8) $a^{-m}=\dfrac{1}{a^m}$ Use rule (1) above to obtain: $=\dfrac{p^{1/5+7/10+1/3}}{(p^3)^{-1/5}} \\=\dfrac{p^{6/30+21/30+10/30}}{(p^3)^{-1/5}} \\=\dfrac{p^{37/30}}{(p^3)^{-1/5}}$ Use rule (7) above to obtain: $\\=\dfrac{p^{37/30}}{p^{3\cdot (-1/5)}} \\=\dfrac{p^{37/30}}{p^{-3/5}}$ Use rule (2) above to obtain: $=p^{37/30-(-3/5)} \\=p^{37/30+3/5} \\=p^{37/30 + 18/30} \\=p^{55/30} \\=\color{blue}{p^{11/6}}$
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