Solve 3e^3f/4ediv4e^7/5f

$$\frac { 3 e ^ { 3 } f } { 4 e } \div \frac { 4 e ^ { 7 } } { 5 f }$$

Evaluate

$$\frac{15f^{2}}{16e^{5}}$$

Solution Steps

Divide \frac{3e^{3}f}{4e} by \frac{4e^{7}}{5f} by multiplying \frac{3e^{3}f}{4e} by the reciprocal of \frac{4e^{7}}{5f}.

$$\frac{3e^{3}f\times 5f}{4e\times 4e^{7}}$$

Cancel out ee^{2} in both numerator and denominator.

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

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

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

Multiply 3 and 5 to get 15.

$$\frac{15f^{2}}{4\times 4e^{5}}$$

Multiply 4 and 4 to get 16.

$$\frac{15f^{2}}{16e^{5}}$$

Differentiate w.r.t. f

$$\frac{15f}{8e^{5}}$$