Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.6 - Properties of Integral Exponents - Exercise Set - Page 81: 147


If $7^{-2}$ is raised to the third power, the result is a number between 0 and 1. --> The statement makes sense.

Work Step by Step

$7^{-2}$ is raised to the third power can be written as: $(7^{-2})^{3}$. Evaluate. Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $$(7^{-2})^{3} = 7^{-6}$$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ Thus, $$7^{-6} = \frac{1}{7^{6}}$$ $\frac{1}{7^{6}}$ is a number that lies between $0$ and $1$; hence, the statement makes sense.
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