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: 56

Answer

$\left(b^8\right)^{-3}=b^{-24} = \dfrac{1}{b^{24}}$

Work Step by Step

RECALL: (i) The power rule of exponents states that: $\left(a^{m}\right)^n=a^{mn}$. (ii) The negative-exponent rule states that: $a^{-m} = \dfrac{1}{a^m}$ and $\dfrac{1}{a^{-m}}=a^m$ where $a \ne 0$. Use the power rule to find: $\left(b^8\right)^{-3}=b^{8(-3)}=b^{-24}$ Use the negative-exponent rule to find: $b^{-24} = \dfrac{1}{b^{24}}$
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