Rewrite the expression without using a negative exponent.
\[
\frac{1}{-4 x^{-2}}
\]
Simplify your answer as much as possible.

Step 1 ：Rewrite the expression \(\frac{1}{-4 x^{-2}}\) without using a negative exponent.

Step 2 ：The expression contains a negative exponent, which means the base (in this case, x) is in the denominator of a fraction. To rewrite the expression without a negative exponent, we need to move the base to the numerator.

Step 3 ：Also, the fraction is divided by -4, which can be simplified by multiplying the numerator by -4.

Step 4 ：So, the expression becomes \(-x^2/4\).

Step 5 ：The expression has been simplified and rewritten without a negative exponent. The base x has been moved to the numerator and the fraction has been simplified by multiplying the numerator by -4.

Step 6 ：Final Answer: The simplified expression without using a negative exponent is \(\boxed{-\frac{x^2}{4}}\).