Solve (xy/2div3/4x^3y^2)^3

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

Evaluate

$$\frac{8y^{9}x^{12}}{27}$$

Solution Steps

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

To raise \frac{2x^{4}y^{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{2^{3}x^{12}\left(y^{3}\right)^{3}}{3^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{12}y^{9}}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8x^{12}y^{9}}{27}$$

Expand

$$\frac{8y^{9}x^{12}}{27}$$

Solution Steps

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

To raise \frac{2x^{4}y^{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{2^{3}x^{12}\left(y^{3}\right)^{3}}{3^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{12}y^{9}}{3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8x^{12}y^{9}}{27}$$