Which statement correctly defines a negative integer exponent for a nonzero base $a$ and positive integer $n$?

$a^{-n}$ gives a negative result when $n$ is odd, and positive when $n$ is even.

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

$a^{-n}=a^n$

$a^{-n}=(-a{)}^n$