Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises - Page 276: 36


a. C. $\frac{1}{64}$ b. D. $-\frac{1}{64}$ c. D. $-\frac{1}{64}$ d. C. $\frac{1}{64}$

Work Step by Step

According to the negative exponent rule, $a^{-n}=\frac{1}{a^{n}}$. Therefore, a. $4^{-3}=\frac{1}{4^{3}}=\frac{1}{4\times4\times4}=\frac{1}{64}$ b. $-4^{-3}=-\frac{1}{4^{3}}=-\frac{1}{4\times4\times4}=-\frac{1}{64}$ c. $(-4)^{-3}=\frac{1}{(-4)^{3}}=\frac{1}{-4\times-4\times-4}=\frac{1}{-64}=-\frac{1}{64}$ d. $-(-4)^{-3}=-\frac{1}{(-4)^{3}}=-\frac{1}{-4\times-4\times-4}=-\frac{1}{-64}=-(-\frac{1}{64})=\frac{1}{64}$
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