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: 52

Answer

$\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}=\dfrac{a^{6}}{b^{9}}$

Work Step by Step

$\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}$ First, we know that $c^{0}=1$. So, this expression can be rewritten as: $\Big(\dfrac{a^{5}bc^{0}}{a^{7}b^{-2}}\Big)^{-3}=\Big(\dfrac{a^{5}b}{a^{7}b^{-2}}\Big)^{-3}=...$ To change the exponent's sign, write the denominator as the numerator and vice versa: $...=\Big(\dfrac{a^{7}b^{-2}}{a^{5}b}\Big)^{3}=...$ Evaluate the exponential expression: $...=\dfrac{a^{21}b^{-6}}{a^{15}b^{3}}=...$ Finally, perform the division and simplify: $...=a^{21-15}b^{-6-3}=a^{6}b^{-9}=\dfrac{a^{6}}{b^{9}}$
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