Solve 5e^4f/3ediv4e^6/5f

$$\frac { 5 e ^ { 4 } f } { 3 e } \div \frac { 4 e ^ { 6 } } { 5 f }$$

Evaluate

$$\frac{25f^{2}}{12e^{3}}$$

Solution Steps

Divide \frac{5e^{4}f}{3e} by \frac{4e^{6}}{5f} by multiplying \frac{5e^{4}f}{3e} by the reciprocal of \frac{4e^{6}}{5f}.

$$\frac{5e^{4}f\times 5f}{3e\times 4e^{6}}$$

Cancel out ee^{3} in both numerator and denominator.

$$\frac{5\times 5ff}{3\times 4e^{3}}$$

Multiply f and f to get f^{2}.

$$\frac{5\times 5f^{2}}{3\times 4e^{3}}$$

Multiply 5 and 5 to get 25.

$$\frac{25f^{2}}{3\times 4e^{3}}$$

Multiply 3 and 4 to get 12.

$$\frac{25f^{2}}{12e^{3}}$$

Differentiate w.r.t. f

$$\frac{25f}{6e^{3}}$$