Answer
$\frac{1}{16}$
Work Step by Step
We start with the given expression: $(-2)^{-4}$
The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{1}{(-2)^4}$
We expand the exponent on the denominator: $\frac{1}{(-2)(-2)(-2)(-2)}=\frac{1}{4\times4}=\frac{1}{16}$
