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 - Page 63: 18

Answer

$\dfrac{1}{125t^3}$

Work Step by Step

RECALL: (1) $a^{-m} = \dfrac{1}{a^m}$ (2) $\dfrac{a^m}{a^n} = a^{m-n}$ (3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$ (4) $(ab)^m = a^mb^m$ Use rule (1) above to obtain: $(5t)^{-3} = \dfrac{1}{(5t)^3}$ Use rule (4) above to obtain: $=\dfrac{1}{5^3t^3} \\=\dfrac{1}{125t^3}$
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