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: 109



Work Step by Step

$$(\frac{−15a^{4}b^{2}}{5a^{10}b^{-3}})^{3}$$ Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $=(\frac{−15a^{4}b^{2}}{5a^{10}b^{-3}})^{3}$ $=(\frac{−3a^{4}b^{2}}{a^{10}b^{-3}})^{3}$ $=\frac{−3^{3}a^{4\cdot 3}b^{2\cdot 3}}{a^{10\cdot 3}b^{-3\cdot 3}}$ $=\frac{−3^{3}a^{12}b^{6}}{a^{30}b^{-9}}$ $=\frac{−27^{3}a^{12}b^{6}}{a^{30}b^{-9}}$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ Hence, $=\frac{−27^{3}a^{12}b^{6}}{a^{30}b^{-9}}$ $=\frac{−27b^{6+9}}{a^{30-12}}$ $=\frac{−27b^{15}}{a^{18}}$
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