Final answer:
The simplified form of (1/4x)⁻² is obtained by taking the reciprocal of the base to remove the negative exponent and then squaring it, resulting in 16x², corresponding to option C).
Step-by-step explanation:
The simplified form of (1/4x)⁻² is found by first recognizing the negative exponent, which indicates that we should take the reciprocal of the base and then raise it to the positive of that exponent. In this case, the base is (1/4x), so we take the reciprocal, which is 4x, and then square it.
Here's the step-by-step simplification:
- (1/4x)⁻² = (4x)²
- (4x)² = 4² * x²
- 4² = 16
- 16 * x² = 16x²
Therefore, the simplified form is 16/x², which matches option C).