Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.6 Exponents - R.6 Exercises - Page R-25: 43



Work Step by Step

$\displaystyle \frac{7^{-1/3}\cdot 7r^{-3}}{7^{2/3}\cdot(r^{-2})^{2}}=$ ... numerator: $a^{m}\cdot a^{n}=a^{m+n}$ , ... denominator: $(a^{m})^{n}=a^{mn}$ ... $=\displaystyle \frac{7^{-1/3+1}r^{-3}}{7^{2/3}r^{-4}}$ = ...... use: $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ $=7^{-1/3+3/3-2/3}\cdot r^{-3-(-4)}$ $=7^{0}r^{-3+4}$ $=1\cdot r^{1}$ $=r$
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