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: 37



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) $(ab)^m = a^mb^m$ (5) $(a^m)^n=a^{mn}$ (6) $a^m \cdot a^n = a^{m+n}$ Use rule (4) above to obtain: $=5^4a^{-1(4)} \cdot a^{2(-3)} \\=5^4a^{-4} \cdot a^{-6}$ Use rule (6) above to obtain: $=5^4a^{-4+(-6)} \\=5^4a^{-10} \\=625a^{-10}$ Use rule (1) above to obtain: $=625 \cdot \dfrac{1}{a^{10}} \\=\color{blue}{\dfrac{625}{a^{10}}}$
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