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: 26

Answer

$\displaystyle \frac{y^{4}}{(xy-1)^{2}}$

Work Step by Step

$(x\cdot y^{-1}-y^{-2})^{-2}$=.........$\displaystyle \frac{1}{a^{n}}=a^{-n}$ $=[\displaystyle \frac{x}{y}-\frac{1}{y^{2}}]^{-2}$=........common denominator =$y^{2}$ $=[\displaystyle \frac{xy}{y^{2}}-\frac{1}{y^{2}}]^{-2}$ $=[\displaystyle \frac{xy-1}{y^{2}}]^{-2}$=.........$\displaystyle \frac{1}{a^{n}}=a^{-n}$ $=[\displaystyle \frac{y^{2}}{xy-1}]^{2}$=.........$(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$ $=\displaystyle \frac{(y^{2})^{2}}{(xy-1)^{2}}$=.........$(a^{m})^{n}=a^{mn}$ $=\displaystyle \frac{y^{4}}{(xy-1)^{2}}$
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