Solve frac{(2x^{3}y^2)^3}{(2xy^2)^2}

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

Evaluate

$$2y^{2}x^{7}$$

Solution Steps

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

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

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

$$\frac{2^{3}x^{9}\left(y^{2}\right)^{3}}{\left(2xy^{2}\right)^{2}}$$

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

$$\frac{2^{3}x^{9}y^{6}}{\left(2xy^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{9}y^{6}}{\left(2xy^{2}\right)^{2}}$$

Expand \left(2xy^{2}\right)^{2}.

$$\frac{8x^{9}y^{6}}{2^{2}x^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{8x^{9}y^{6}}{2^{2}x^{2}y^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{8x^{9}y^{6}}{4x^{2}y^{4}}$$

Cancel out 4x^{2}y^{4} in both numerator and denominator.

$$2y^{2}x^{7}$$

Expand

$$2y^{2}x^{7}$$

Solution Steps

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

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

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

$$\frac{2^{3}x^{9}\left(y^{2}\right)^{3}}{\left(2xy^{2}\right)^{2}}$$

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

$$\frac{2^{3}x^{9}y^{6}}{\left(2xy^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{9}y^{6}}{\left(2xy^{2}\right)^{2}}$$

Expand \left(2xy^{2}\right)^{2}.

$$\frac{8x^{9}y^{6}}{2^{2}x^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{8x^{9}y^{6}}{2^{2}x^{2}y^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{8x^{9}y^{6}}{4x^{2}y^{4}}$$

Cancel out 4x^{2}y^{4} in both numerator and denominator.

$$2y^{2}x^{7}$$