Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set: 51

Answer

$\Big(\dfrac{x^{-2}y^{4}z^{0}}{x^{3}y^{7}}\Big)^{2}=\dfrac{1}{x^{10}y^{6}}$

Work Step by Step

$\Big(\dfrac{x^{-2}y^{4}z^{0}}{x^{3}y^{7}}\Big)^{2}$ First, note that $z^{0}=1$, so this expression can be rewritten as: $\Big(\dfrac{x^{-2}y^{4}z^{0}}{x^{3}y^{7}}\Big)^{2}=\Big(\dfrac{x^{-2}y^{4}}{x^{3}y^{7}}\Big)^{2}=...$ Evaluate the exponential expression: $...=\dfrac{x^{-4}y^{8}}{x^{6}y^{14}}=...$ Evaluate the division: $...=x^{-4-6}y^{8-14}=x^{-10}y^{-6}=\dfrac{1}{x^{10}y^{6}}$
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