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: 99


Yes, $a=-1$ or $a=1$

Work Step by Step

We know that $a^{-1}=\frac{1}{a}$. So, if we know that $a^{-1}=a^{1}$, then we also know that $a=\frac{1}{a}$ for some number a. Therefore, the number a will have to have the same value as its reciprocal, and we know that -1 and 1 are the only numbers that satisfy this condition. Therefore, $a=-1$ or $a=1$.
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