Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set: 18

Answer

$\frac{64}{p^{9}}$

Work Step by Step

We are given the expression $(\frac{4p^{6}}{p^{9}})^{3}$. First, we can use the power rule to simplify. $(\frac{4p^{6}}{p^{9}})^{3}=\frac{(4p^{6})^{3}}{(p^{9})^{3}}=\frac{4^{3}p^{6\times3}}{p^{9\times3}}=\frac{64p^{18}}{p^{27}}$ Next, we can use the quotient rule. $64\times(p^{18-27})=64p^{-9}=\frac{64}{p^{9}}$
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