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: 110



Work Step by Step

$$(\frac{−30a^{14}b^{8}}{10a^{17}b^{-2}})^{3}$$ Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $=(\frac{−30a^{14}b^{8}}{10a^{17}b^{-2}})^{3}$ $=(\frac{−3a^{14}b^{8}}{a^{17}b^{-2}})^{3}$$=\frac{−3^{3}a^{14\cdot 3}b^{8\cdot 3}}{a^{17\cdot 3}b^{-2\cdot 3}}$ $=\frac{−27a^{42}b^{24}}{a^{51}b^{-6}}$ Recall the quotient rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$ and $\frac{a^{n}}{a^{m}}=\frac{1}{a^{m+n}}$ if $m>n$ Thus, $=\frac{−27a^{42}b^{24}}{a^{51}b^{-6}}$ $=\frac{−27b^{24+6}}{a^{51-42}}$ $=\frac{−27b^{30}}{a^{9}}$
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