Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set: 70

Answer

$\dfrac{(a^{6}b^{-2})^{4}}{(4a^{-3}b^{-3})^{3}}=\dfrac{a^{33}b}{64}$

Work Step by Step

$\dfrac{(a^{6}b^{-2})^{4}}{(4a^{-3}b^{-3})^{3}}$ Evaluate the exponential expressions in the numerator and the denominator: $\dfrac{(a^{6}b^{-2})^{4}}{(4a^{-3}b^{-3})^{3}}=\dfrac{a^{24}b^{-8}}{64a^{-9}b^{-9}}=...$ Evaluate the division and simplify: $...=\dfrac{1}{64}a^{24-(-9)}b^{-8-(-9)}=\dfrac{1}{64}a^{33}b=\dfrac{a^{33}b}{64}$
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