To find the expression equivalent to [tex]\(\frac{4 f^2}{3} \div \frac{1}{4 f}\)[/tex], we'll simplify the given division by following these steps:
1. Rewrite the division as multiplication by the reciprocal:
When dividing by a fraction, we multiply by the reciprocal of that fraction. So we have:
[tex]\[
\frac{4 f^2}{3} \div \frac{1}{4 f} = \frac{4 f^2}{3} \times \frac{4 f}{1}
\][/tex]
2. Simplify the multiplication:
Now, we can directly multiply the numerators together and the denominators together:
[tex]\[
\frac{4 f^2}{3} \times \frac{4 f}{1} = \frac{4 f^2 \cdot 4 f}{3 \cdot 1}
\][/tex]
3. Multiply the numerators:
[tex]\[
4 f^2 \cdot 4 f = 16 f^3
\][/tex]
4. Multiply the denominators:
[tex]\[
3 \cdot 1 = 3
\][/tex]
Therefore, our simplified expression is:
[tex]\[
\frac{16 f^3}{3}
\][/tex]
Thus, the expression equivalent to [tex]\(\frac{4 f^2}{3} \div \frac{1}{4 f}\)[/tex] is:
[tex]\[
\boxed{\frac{16 f^3}{3}}
\][/tex]
