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: 84



Work Step by Step

To solve $(\frac{a^{-3}}{b^{5}})^{-4}$, RECALL: (i) The quotients-to-powers rule states that: $(\frac{a}{b})^n=\frac{a^n}{b^n}$ (ii) The power-rule states that $(a^m)^n=a^{mn}$ (iii) The negative-exponent rule states that: $a^{−m} =\frac{1}{a^m}$ and $\frac{1}{a^{-m}} = a^{m}$ Hence, using quotients-to-powers rule and power rule: $(\frac{a^{-3}}{b^{5}})^{-4}$ = $\frac{(a^{-3})^{-4}}{(b^{5})^{-4}}$ Using the power rule: $=\frac{a^{-3(-4)}}{b^{5(-4)}}$ $=\frac{a^{12}}{b^{-20}}$ Using negative-exponent rule, $=\frac{a^{12}}{b^{-20}}= a^{12}b^{20}$
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