Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Practice and Problem-Solving Exercises - Page 423: 72


$n=1$ or $n=-1$

Work Step by Step

Given: $n^{-3}=\frac{1}{n^3}$ and $(\frac{1}{n})^5=\frac{1}{n^5}$ Set two equations equal to each other: $\frac{1}{n^3}=\frac{1}{n^5}$ Solve for $n$: $n^5=n^3$ $n^5-n^3=0$ $n^3(n^2-1)=0$ $n^3=0$ or $n^2-1=0$ $n=0$ or $n=\pm1$ Since $n$ cannot be $0$, the solutions are $n=1$ or $n=-1$.
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