College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises - Page 76: 87



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $ \left( -\dfrac{5}{4} \right)^{-2} .$ $\bf{\text{Solution Details:}}$ Since $\left( \dfrac{x}{y} \right)^m=\dfrac{x^m}{y^m},$ then the expression above is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{-5}{4} \right)^{-2} \\\\= \dfrac{(-5)^{-2}}{4^{-2}} .\end{array} Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{4^{2}}{(-5)^{2}} \\\\= \dfrac{16}{25} .\end{array}
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