Solve frac{(2x^{3}y^2)^4}{(5x^2y)^2}

$$\frac { ( 2 x ^ { 3 } y ^ { 2 } ) ^ { 4 } } { ( 5 x ^ { 2 } y ) ^ { 2 } }$$

Evaluate

$$\frac{16y^{6}x^{8}}{25}$$

Solution Steps

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

$$\frac{2^{4}\left(x^{3}\right)^{4}\left(y^{2}\right)^{4}}{\left(5x^{2}y\right)^{2}}$$

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

$$\frac{2^{4}x^{12}\left(y^{2}\right)^{4}}{\left(5x^{2}y\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{2^{4}x^{12}y^{8}}{\left(5x^{2}y\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{12}y^{8}}{\left(5x^{2}y\right)^{2}}$$

Expand \left(5x^{2}y\right)^{2}.

$$\frac{16x^{12}y^{8}}{5^{2}\left(x^{2}\right)^{2}y^{2}}$$

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

$$\frac{16x^{12}y^{8}}{5^{2}x^{4}y^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{16x^{12}y^{8}}{25x^{4}y^{2}}$$

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

$$\frac{16y^{6}x^{8}}{25}$$

Expand

$$\frac{16y^{6}x^{8}}{25}$$

Solution Steps

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

$$\frac{2^{4}\left(x^{3}\right)^{4}\left(y^{2}\right)^{4}}{\left(5x^{2}y\right)^{2}}$$

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

$$\frac{2^{4}x^{12}\left(y^{2}\right)^{4}}{\left(5x^{2}y\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{2^{4}x^{12}y^{8}}{\left(5x^{2}y\right)^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{12}y^{8}}{\left(5x^{2}y\right)^{2}}$$

Expand \left(5x^{2}y\right)^{2}.

$$\frac{16x^{12}y^{8}}{5^{2}\left(x^{2}\right)^{2}y^{2}}$$

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

$$\frac{16x^{12}y^{8}}{5^{2}x^{4}y^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{16x^{12}y^{8}}{25x^{4}y^{2}}$$

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

$$\frac{16y^{6}x^{8}}{25}$$