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: 50

Answer

$\frac{1}{y^{14}}$

Work Step by Step

We are given the expression $\frac{y^{-7}y}{y^{-8}}$. To simplify, we can first use the product rule, which holds that $a^{m}\times a^{n}=a^{m+n}$. $\frac{y^{-7+1}}{y^{-8}}=\frac{y^{-6}}{y^{8}}$ Next, we can use the quotient rule, which holds that $\frac{a^{m}}{a^{n}}=a^{m-n}$. $y^{-6-8}=y^{-14}$ Finally, we know that $a^{-n}=\frac{1}{a^{n}}$, so $y^{-14}=\frac{1}{y^{14}}$
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