## Algebra 1

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 $a^{n}$
$a^{n}$ $\times$ $a^{-n}$ = $a^{n}$ $\times$ $\frac{1}{a^{n}}$ = 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.