Answer
$-\displaystyle \frac{1}{4x^{2}}$
Work Step by Step
... Apply rule $\displaystyle \quad a^{-n}=\frac{1}{a^{n}}$
$(-4x^{2})^{-1}=\displaystyle \frac{1}{\left(-4x^{2}\right)^1}=-\frac{1}{4x^{2}}$
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