Question

Which expression is equivalent to 4f² / (1/4f)?
1) 16f³
2) 16f
3) 16f²
4) 16

Answer 1

The equivalent expression to 4f² / (1/4f) is found by multiplying the numerator and denominator by the reciprocal of the denominator, resulting in 16f³, which is option 1).

Step-by-step explanation:

The student has asked which expression is equivalent to 4f² / (1/4f). To find the equivalent expression, we can simplify by multiplying both the numerator and the denominator by 4f, which is the reciprocal of the denominator.

Here's the step-by-step simplification:

1. Multiply the numerator and denominator by 4f: (4f² × 4f) / ((1/4f) × 4f).
2. Simplify the denominator: 4f × (1/4f) = 1, so the denominator is now 1.
3. Multiply out the numerator: 4f² × 4f = 16f³.
4. Since the denominator is 1, we are left with the numerator only: 16f³.

Therefore, the expression equivalent to 4f² / (1/4f) is 16f³, which corresponds to option 1).