## Algebra 1: Common Core (15th Edition)

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 $a^{n}$
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.