Solve 9x^2/y(4x/9ydiv3y^2/2)

$$\frac { 9 x ^ { 2 } } { y } ( \frac { 4 x } { 9 y } \div \frac { 3 y ^ { 2 } } { 2 } )$$

Evaluate

$$\frac{8x^{3}}{3y^{4}}$$

Solution Steps

Divide \frac{4x}{9y} by \frac{3y^{2}}{2} by multiplying \frac{4x}{9y} by the reciprocal of \frac{3y^{2}}{2}.

$$\frac{9x^{2}}{y}\times \frac{4x\times 2}{9y\times 3y^{2}}$$

Multiply 4 and 2 to get 8.

$$\frac{9x^{2}}{y}\times \frac{8x}{9y\times 3y^{2}}$$

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

$$\frac{9x^{2}}{y}\times \frac{8x}{9y^{3}\times 3}$$

Multiply 9 and 3 to get 27.

$$\frac{9x^{2}}{y}\times \frac{8x}{27y^{3}}$$

Multiply \frac{9x^{2}}{y} times \frac{8x}{27y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9x^{2}\times 8x}{y\times 27y^{3}}$$

Cancel out 9 in both numerator and denominator.

$$\frac{8xx^{2}}{3yy^{3}}$$

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

$$\frac{8x^{3}}{3yy^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{8x^{3}}{3y^{4}}$$

Differentiate w.r.t. x

$$\frac{8x^{2}}{y^{4}}$$