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 80: 67



Work Step by Step

RECALL: (i) The products-to-powers rule states that: $(ab)^n=a^nb^n$ (ii) The power rule states that: $(a^m)^n=a^{mn}$ (iii) The negative-exponent rule states that: $a^{-m} = \dfrac{1}{a^m}$ and $\dfrac{1}{a^{-m}} = a^m$ Use the products-to-powers rule to find: $=(-3)^{-3}(x^{-2})^{-3}$ Use the power rule to find: $=(-3)^{-3}x^{-2(-3)} \\=(-3)^{-3}x^{6}$ Use the negative-exponent rule to find: $=\frac{1}{(-3)^3}\cdot x^{6} \\=\frac{1}{-27} \cdot x^6 \\=-\frac{x^6}{27}$
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