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: 41


$\displaystyle \frac{x^{4}}{y^{4}}$

Work Step by Step

$[\displaystyle \frac{x^{6}y^{-3}}{x^{-2}y^{5}}]^{1/2}$ =......use: $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ $=[x^{6-(-2)}\cdot y^{-3-5}]^{1/2}$ $=[x^{8}\cdot y^{-8}]^{1/2}$ =......use: $(ab)^{m}=a^{m}b^{m}$ $=(x^{8})^{1/2}(y^{-8})^{1/2}$ =......use: $(a^{m})^{n}=a^{mn}$ $=x^{4}y^{-4}$ =......use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$ $= \displaystyle \frac{x^{4}}{y^{4}}$
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