Question
The multiplicative inverse of $(-4)^{-2}$ is $(4)^{-2}$.

Answer

$a$ is called the multiplicative inverse of b, if $a \times b = 1.$
Put $b = (-4)^{-2}$
$\therefore$ $a × (-4)^{-2}= 1$
$\Rightarrow\text{a}=\frac{1}{(-4)^{-2}}=(-4)^2$

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