Solve (2x/3y^2)^3div(4x^3/3y)^2=

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

Evaluate

$$\frac{1}{6x^{3}y^{4}}$$

Solution Steps

To raise \frac{2x}{3y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}}}{\left(\frac{4x^{3}}{3y}\right)^{2}}$$

To raise \frac{4x^{3}}{3y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}}}{\frac{\left(4x^{3}\right)^{2}}{\left(3y\right)^{2}}}$$

Divide \frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}} by \frac{\left(4x^{3}\right)^{2}}{\left(3y\right)^{2}} by multiplying \frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}} by the reciprocal of \frac{\left(4x^{3}\right)^{2}}{\left(3y\right)^{2}}.

$$\frac{\left(2x\right)^{3}\times \left(3y\right)^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Expand \left(2x\right)^{3}.

$$\frac{2^{3}x^{3}\times \left(3y\right)^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}\times \left(3y\right)^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Expand \left(3y\right)^{2}.

$$\frac{8x^{3}\times 3^{2}y^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8x^{3}\times 9y^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Multiply 8 and 9 to get 72.

$$\frac{72x^{3}y^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Expand \left(3y^{2}\right)^{3}.

$$\frac{72x^{3}y^{2}}{3^{3}\left(y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{72x^{3}y^{2}}{3^{3}y^{6}\times \left(4x^{3}\right)^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{72x^{3}y^{2}}{27y^{6}\times \left(4x^{3}\right)^{2}}$$

Expand \left(4x^{3}\right)^{2}.

$$\frac{72x^{3}y^{2}}{27y^{6}\times 4^{2}\left(x^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{72x^{3}y^{2}}{27y^{6}\times 4^{2}x^{6}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{72x^{3}y^{2}}{27y^{6}\times 16x^{6}}$$

Multiply 27 and 16 to get 432.

$$\frac{72x^{3}y^{2}}{432y^{6}x^{6}}$$

Cancel out 72y^{2}x^{3} in both numerator and denominator.

$$\frac{1}{6x^{3}y^{4}}$$

Expand

$$\frac{1}{6x^{3}y^{4}}$$

Solution Steps

To raise \frac{2x}{3y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}}}{\left(\frac{4x^{3}}{3y}\right)^{2}}$$

To raise \frac{4x^{3}}{3y} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}}}{\frac{\left(4x^{3}\right)^{2}}{\left(3y\right)^{2}}}$$

Divide \frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}} by \frac{\left(4x^{3}\right)^{2}}{\left(3y\right)^{2}} by multiplying \frac{\left(2x\right)^{3}}{\left(3y^{2}\right)^{3}} by the reciprocal of \frac{\left(4x^{3}\right)^{2}}{\left(3y\right)^{2}}.

$$\frac{\left(2x\right)^{3}\times \left(3y\right)^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Expand \left(2x\right)^{3}.

$$\frac{2^{3}x^{3}\times \left(3y\right)^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}\times \left(3y\right)^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Expand \left(3y\right)^{2}.

$$\frac{8x^{3}\times 3^{2}y^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8x^{3}\times 9y^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Multiply 8 and 9 to get 72.

$$\frac{72x^{3}y^{2}}{\left(3y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

Expand \left(3y^{2}\right)^{3}.

$$\frac{72x^{3}y^{2}}{3^{3}\left(y^{2}\right)^{3}\times \left(4x^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{72x^{3}y^{2}}{3^{3}y^{6}\times \left(4x^{3}\right)^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{72x^{3}y^{2}}{27y^{6}\times \left(4x^{3}\right)^{2}}$$

Expand \left(4x^{3}\right)^{2}.

$$\frac{72x^{3}y^{2}}{27y^{6}\times 4^{2}\left(x^{3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{72x^{3}y^{2}}{27y^{6}\times 4^{2}x^{6}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{72x^{3}y^{2}}{27y^{6}\times 16x^{6}}$$

Multiply 27 and 16 to get 432.

$$\frac{72x^{3}y^{2}}{432y^{6}x^{6}}$$

Cancel out 72y^{2}x^{3} in both numerator and denominator.

$$\frac{1}{6x^{3}y^{4}}$$