Solve frac{(2xy)^{3}(4x^{3}y^{2})^2}{(2x^2y^3)^2}

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

Evaluate

$$32yx^{5}$$

Solution Steps

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

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

$$\frac{8x^{3}y^{3}\times 4^{2}x^{6}\left(y^{2}\right)^{2}}{\left(2x^{2}y^{3}\right)^{2}}$$

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

$$\frac{8x^{3}y^{3}\times 4^{2}x^{6}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8x^{3}y^{3}\times 16x^{6}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

Multiply 8 and 16 to get 128.

$$\frac{128x^{3}y^{3}x^{6}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{128x^{9}y^{3}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{128x^{9}y^{7}}{\left(2x^{2}y^{3}\right)^{2}}$$

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

$$\frac{128x^{9}y^{7}}{2^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}$$

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

$$\frac{128x^{9}y^{7}}{2^{2}x^{4}\left(y^{3}\right)^{2}}$$

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

$$\frac{128x^{9}y^{7}}{2^{2}x^{4}y^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{128x^{9}y^{7}}{4x^{4}y^{6}}$$

Cancel out 4x^{4}y^{6} in both numerator and denominator.

$$32yx^{5}$$

Expand

$$32yx^{5}$$

Solution Steps

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

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

Calculate 2 to the power of 3 and get 8.

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

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

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

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

$$\frac{8x^{3}y^{3}\times 4^{2}x^{6}\left(y^{2}\right)^{2}}{\left(2x^{2}y^{3}\right)^{2}}$$

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

$$\frac{8x^{3}y^{3}\times 4^{2}x^{6}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8x^{3}y^{3}\times 16x^{6}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

Multiply 8 and 16 to get 128.

$$\frac{128x^{3}y^{3}x^{6}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{128x^{9}y^{3}y^{4}}{\left(2x^{2}y^{3}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{128x^{9}y^{7}}{\left(2x^{2}y^{3}\right)^{2}}$$

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

$$\frac{128x^{9}y^{7}}{2^{2}\left(x^{2}\right)^{2}\left(y^{3}\right)^{2}}$$

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

$$\frac{128x^{9}y^{7}}{2^{2}x^{4}\left(y^{3}\right)^{2}}$$

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

$$\frac{128x^{9}y^{7}}{2^{2}x^{4}y^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{128x^{9}y^{7}}{4x^{4}y^{6}}$$

Cancel out 4x^{4}y^{6} in both numerator and denominator.

$$32yx^{5}$$