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 - Page 245: 125


$(-17)^{-8}$ is positive because when the negative exponent rule is applied, the denominator's power is even (which is $8$). Any non-zero real number raised to an even power is positive. Refer to the step-by-step part below for a detailed explanation.

Work Step by Step

RECALL: For any nonzero real number $a$, $a^m$ is positive when $m$ is an even integer. The reason for this is that an even power $m$ means there are $\frac{m}{2}$ pairs of identical factors. Since the product of two numbers with the same sign is positive, then having $\frac{m}{2}$ pairs of identical factors means that the product will surely be positive. Note that $a^{-m} = \dfrac{1}{a^m}, m \ne 0$. Applying this to $(-17)^{-8}$ gives $\dfrac{1}{(-17)^8}$. Since the denominator involves an even power of $-17$, then the denominator is positive. Thus, the quotient will also be positive as the quotient of two positive numbers is positive.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.