Algebra 1

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

Chapter 7 - Exponents and Exponential Functions - 7-3 Multipying Powers with the Same Base - Practice and Problem-Solving Exercises - Page 430: 43


$a^{-4}\times a^{4}=1$

Work Step by Step

$a^{?}\times a^{4}=1$ The zero as an exponent rule states that for every nonzero number $a$, $a^0=1$. Therefore, $a^{?}\times a^{4}=a^0$ To multiply powers with the same base, we add the exponents. When we add $4$ and the first exponent, we must get $0$. The only way this is true is if the first exponent is $-4$ because $4+(-4)=0$. Therefore, $a^{-4}\times a^{4}=a^0$ We rewrite the equation in its original form: $a^{-4}\times a^{4}=1$
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