Solve 2xt/3div(x/4tdiv2t/3)

$$\frac { 2 x t } { 3 } \div ( \frac { x } { 4 t } \div \frac { 2 t } { 3 } )$$

Evaluate

$$\frac{16t^{3}}{9}$$

Short Solution Steps

Divide \frac{2xt}{3} by \frac{\frac{x}{4t}}{\frac{2t}{3}} by multiplying \frac{2xt}{3} by the reciprocal of \frac{\frac{x}{4t}}{\frac{2t}{3}}.

$$\frac{2xt\times \frac{2t}{3}}{3\times \frac{x}{4t}}$$

Express 2\times \frac{2t}{3} as a single fraction.

$$\frac{\frac{2\times 2t}{3}xt}{3\times \frac{x}{4t}}$$

Express 3\times \frac{x}{4t} as a single fraction.

$$\frac{\frac{2\times 2t}{3}xt}{\frac{3x}{4t}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{4t}{3}xt}{\frac{3x}{4t}}$$

Express \frac{4t}{3}x as a single fraction.

$$\frac{\frac{4tx}{3}t}{\frac{3x}{4t}}$$

Express \frac{4tx}{3}t as a single fraction.

$$\frac{\frac{4txt}{3}}{\frac{3x}{4t}}$$

Divide \frac{4txt}{3} by \frac{3x}{4t} by multiplying \frac{4txt}{3} by the reciprocal of \frac{3x}{4t}.

$$\frac{4txt\times 4t}{3\times 3x}$$

Cancel out x in both numerator and denominator.

$$\frac{4\times 4ttt}{3\times 3}$$

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

$$\frac{4\times 4t^{2}t}{3\times 3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{4\times 4t^{3}}{3\times 3}$$

Multiply 4 and 4 to get 16.

$$\frac{16t^{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{16t^{3}}{9}$$

Differentiate w.r.t. t

$$\frac{16t^{2}}{3}$$