Answer
False
A corrected statement would be: $(-2)^4=2^{4}$
Work Step by Step
The statement is false because:
$(-2)^4 = 16$
$2^{-4} = \dfrac{1}{2^4} = \dfrac{1}{16}$
Thus,
$(-2)^4 \ne 2^{-4}$
A corrected statement would be:
$(-2)^4=2^{4}$