Question

which expression is equivalent to \\(\frac{4f^2}{3} \div \frac{1}{4f}\\)? \\(\frac{16f^3}{3}\\) \\(\frac{f}{3}\\) \\(\frac{3}{16f^3}\\) \\(\frac{3}{f}\\)

Explanation:

Step1: Recall division of fractions rule

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{4f^2}{3} \div \frac{1}{4f}=\frac{4f^2}{3} \times 4f\).

Step2: Multiply the numerators and denominators

Multiply the numerators: \(4f^2\times4f = 16f^{3}\) (using the rule \(a^m\times a^n=a^{m + n}\), here \(f^2\times f=f^{2 + 1}=f^3\) and \(4\times4 = 16\)). The denominator remains \(3\). So the result is \(\frac{16f^{3}}{3}\).

Answer:

\(\frac{16f^{3}}{3}\) (the first option)