Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Practice and Problem-Solving Exercises - Page 418: 61

Answer

a) The multiplication of $a^{n}$ $\times$ $a^{-n}$ = 1 b) The relationship between $a^{n}$ and $a^{-n}$ is that $a^{-n}$ is the reciprocal of $a^{n}$
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Work Step by Step

$a^{n}$ $\times$ $a^{-n}$ = $a^{n}$ $\times$ $\frac{1}{a^{n}}$ = 1 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 bring the base with the exponent from numerator to denominator if on top or from denominator to numerator if on bottom.
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