Solve 4x^2/3ydivx/12y^3div-2/9xy

$$\frac { 4 x ^ { 2 } } { 3 y } \div \frac { x } { 12 y ^ { 3 } } \div - \frac { 2 } { 9 x y }$$

Evaluate

$$-72x^{2}y^{3}$$

Solution Steps

Divide \frac{4x^{2}}{3y} by \frac{x}{12y^{3}} by multiplying \frac{4x^{2}}{3y} by the reciprocal of \frac{x}{12y^{3}}.

$$\frac{\frac{4x^{2}\times 12y^{3}}{3yx}}{-\frac{2}{9xy}}$$

Cancel out 3xy in both numerator and denominator.

$$\frac{4\times 4xy^{2}}{-\frac{2}{9xy}}$$

Multiply 4 and 4 to get 16.

$$\frac{16xy^{2}}{-\frac{2}{9xy}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-16xy^{2}}{\frac{2}{9xy}}$$

Divide -16xy^{2} by \frac{2}{9xy} by multiplying -16xy^{2} by the reciprocal of \frac{2}{9xy}.

$$\frac{-16xy^{2}\times 9xy}{2}$$

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

$$\frac{-16x^{2}y^{2}\times 9y}{2}$$

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

$$\frac{-16x^{2}y^{3}\times 9}{2}$$

Multiply -16 and 9 to get -144.

$$\frac{-144x^{2}y^{3}}{2}$$

Divide -144x^{2}y^{3} by 2 to get -72x^{2}y^{3}.

$$-72x^{2}y^{3}$$

Differentiate w.r.t. x

$$-144xy^{3}$$