Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 0 - Section 0.2 - Exponents and Radicals - Exercises: 30

Answer

$x^{3}y^{3}z^{3}$

Work Step by Step

group like terms $(\displaystyle \frac{xy^{-2}}{x^{2}y^{-1}z})^{-3}=(\frac{x}{x^{2}}\cdot\frac{y^{-2}}{y^{-1}}\cdot\frac{1}{z})^{-3}=$ ... use: $(\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}),\qquad (\frac{1}{z}=z^{-1})$ ... $= (x^{1-2}y^{-2-(-1)}z^{-1})^{-3} = (x^{-1}\cdot y^{-1}\cdot z^{-1})^{-3}$ ... use $(ab)^{n}=a^{n}b^{n}$ $= x^{-1(-3)}\cdot y^{-1(-3)}\cdot z^{-1(-3)}$ $=x^{3}y^{3}z^{3}$
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