$(ab)^{-n} = a^{-n} \cdot b^{-n}$ for nonzero $a, b$

$a^{-n} = \frac{1}{a^n}$ for any nonzero $a$ and positive integer $n$

$a^{-n} = -a^n$ for any nonzero $a$ and positive integer $n$

$\frac{1}{a^{-n}} = a^{n}$ for any nonzero $a$