Solve 4xy^2/45div8y/27x/frac{9xy{10}}

$$\frac{ 4x { y }^{ 2 } }{ 45 } \div \frac{ \frac{ 8y }{ 27x } }{ \frac{ 9xy }{ 10 } }$$

Evaluate

$$\frac{27y^{2}x^{3}}{100}$$

Solution Steps

Divide \frac{4xy^{2}}{45} by \frac{\frac{8y}{27x}}{\frac{9xy}{10}} by multiplying \frac{4xy^{2}}{45} by the reciprocal of \frac{\frac{8y}{27x}}{\frac{9xy}{10}}.

$$\frac{4xy^{2}\times \frac{9xy}{10}}{45\times \frac{8y}{27x}}$$

Express 4\times \frac{9xy}{10} as a single fraction.

$$\frac{\frac{4\times 9xy}{10}xy^{2}}{45\times \frac{8y}{27x}}$$

Express 45\times \frac{8y}{27x} as a single fraction.

$$\frac{\frac{4\times 9xy}{10}xy^{2}}{\frac{45\times 8y}{27x}}$$

Cancel out 9 in both numerator and denominator.

$$\frac{\frac{4\times 9xy}{10}xy^{2}}{\frac{5\times 8y}{3x}}$$

Multiply 4 and 9 to get 36.

$$\frac{\frac{36xy}{10}xy^{2}}{\frac{5\times 8y}{3x}}$$

Divide 36xy by 10 to get \frac{18}{5}xy.

$$\frac{\frac{18}{5}xyxy^{2}}{\frac{5\times 8y}{3x}}$$

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

$$\frac{\frac{18}{5}x^{2}yy^{2}}{\frac{5\times 8y}{3x}}$$

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

$$\frac{\frac{18}{5}x^{2}y^{3}}{\frac{5\times 8y}{3x}}$$

Multiply 5 and 8 to get 40.

$$\frac{\frac{18}{5}x^{2}y^{3}}{\frac{40y}{3x}}$$

Divide \frac{18}{5}x^{2}y^{3} by \frac{40y}{3x} by multiplying \frac{18}{5}x^{2}y^{3} by the reciprocal of \frac{40y}{3x}.

$$\frac{\frac{18}{5}x^{2}y^{3}\times 3x}{40y}$$

Cancel out y in both numerator and denominator.

$$\frac{3\times \frac{18}{5}xx^{2}y^{2}}{40}$$

Divide 3\times \frac{18}{5}xx^{2}y^{2} by 40 to get 3\times \frac{9}{100}xx^{2}y^{2}.

$$3\times \frac{9}{100}xx^{2}y^{2}$$

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

$$3\times \frac{9}{100}x^{3}y^{2}$$

Multiply 3 and \frac{9}{100} to get \frac{27}{100}.

$$\frac{27}{100}x^{3}y^{2}$$

Differentiate w.r.t. x

$$\frac{81\left(xy\right)^{2}}{100}$$