Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.2 - Exponents and Scientific Notation - Exercise Set: 62

Answer

$\frac{-27b^{30}}{a^{9}}$

Work Step by Step

Start with the given expression: $(\frac{-30a^{14}b^8}{10a^{17}b^{-2}})^{3}$ Remove parentheses: $\frac{(-30)^3(a^{14})^3(b^8)^3}{10^3(a^{17})^3(b^{-2})^3}$ Use power rule to simplify numerator and denominator: $\frac{-27000a^{42}b^{24}}{1000a^{51}b^{-6}}$ Use quotient rule to simplify fraction: $-27a^{-9}b^{30}$ Use negative exponent rule to simplify completely: $\frac{-27b^{30}}{a^{9}}$
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