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 422: 62


a) The multiplication of $a^{n}$ × $a^{-n}$ = 1 b) The relationship between $a^{n}$ and $a^{-n}$ is that $a^{-n}$ is the reciprocal of $a^{n}$

Work Step by Step

A. = $a^{n}$ × $a^{-n}$ =$a^{n}$ × $\frac{1}{a^{n}}$ = 1 B. The main reason why $a^{-n}$ becomes $\frac{1}{a^{n}}$ is that if you have a negative exponent, the only way to make the exponent positive is to take the reciprocal of the actual function and to bring the base with the exponent from numerator to denominator or from denominator to numerator to change the sign of the exponent.
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