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: 105

Answer

$\dfrac{8a^9c^{12}}{b}$

Work Step by Step

RECALL: (i) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne0$ (ii) $a^{-m} = \dfrac{1}{a^m}, a \ne0$ Divide the coefficients by each other and the variables by each other to obtain: $=\dfrac{-24}{-3} \cdot a^{3-(-6)}b^{-5-(-4)}c^{5-(-7)} \\=8 \cdot a^{3+6}b^{-5+4}c^{5+7} \\=8a^{9}b^{-1}c^{12}$ Use rule (ii) above to obtain: $=8a^9 \cdot \dfrac{1}{b} \cdot c^{12} \\=\dfrac{8a^9c^{12}}{b}$
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