Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.2 Negative Exponents and Scientific Notations - 4.2 Exercise Set: 126

Answer

$x^{-n}$ will be negative when: $n$ is an odd integer and $x$ is a negative integer

Work Step by Step

RECALL: $x^{-n}=\dfrac{1}{x^n}, x \ne 0$ Note that when $n$ is even, the value of $\dfrac{1}{x^n}$ where $x\ne0$ will always be positive regardless of the value of $x$. $\dfrac{1}{x^n}$ will only be a negative integer if $n$ is an odd integer and $x$ a is negative integer. Example: $(-5)^{-3} = \dfrac{1}{(-5)^3} = \dfrac{1}{-125} = -\dfrac{1}{125}$ Thus, $x^{-n}$ will be negative when $n$ is odd and $x$ is a negative integer.
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