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: 106

Answer

$\dfrac{3a^7c^{11}}{b}$

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: $=\dfrac{-24}{-8} \cdot a^{2-(-5)}b^{-2-(-1)}c^{8-(-3)} \\=3 \cdot a^{2+5}b^{-2+1}c^{8+3} \\=3a^{7}b^{-1}c^{11}$ Use rule (ii) above to obtain: $=3a^7 \cdot \dfrac{1}{b} \cdot c^{11} \\=\dfrac{3a^7c^{11}}{b}$
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