Intermediate Algebra (6th Edition)

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

Chapter 5 - Section 5.1 - Exponents and Scientific Notation - Exercise Set: 51

Answer

$\frac{b^{7}}{9a^{7}}$

Work Step by Step

We are given the expression $\frac{2a^{-6}b^{2}}{18ab^{-5}}$. We can use the quotient rule to simplify. $\frac{2a^{-6}b^{2}}{18ab^{-5}}=\frac{2}{18}\times(a^{-6-1})\times(b^{2-(-5)})=\frac{1}{9}a^{-7}b^{7}$ We know that $a^{-n}=\frac{1}{a^{n}}$, so this expression further simplifies to $\frac{b^{7}}{9a^{7}}$.
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