Solve frac{(-x^{5}y^{7})^2}{(2x^2y^3)^4}

$$\frac { ( - x ^ { 5 } y ^ { 7 } ) ^ { 2 } } { ( 2 x ^ { 2 } y ^ { 3 } ) ^ { 4 } }$$

Evaluate

$$\frac{\left(xy\right)^{2}}{16}$$

Solution Steps

Expand \left(\left(-x^{5}\right)y^{7}\right)^{2}.

$$\frac{\left(-x^{5}\right)^{2}\left(y^{7}\right)^{2}}{\left(2x^{2}y^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\left(-x^{5}\right)^{2}y^{14}}{\left(2x^{2}y^{3}\right)^{4}}$$

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

$$\frac{\left(x^{5}\right)^{2}y^{14}}{\left(2x^{2}y^{3}\right)^{4}}$$

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

$$\frac{\left(x^{5}\right)^{2}y^{14}}{2^{4}\left(x^{2}\right)^{4}\left(y^{3}\right)^{4}}$$

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

$$\frac{\left(x^{5}\right)^{2}y^{14}}{2^{4}x^{8}\left(y^{3}\right)^{4}}$$

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

$$\frac{\left(x^{5}\right)^{2}y^{14}}{2^{4}x^{8}y^{12}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(x^{5}\right)^{2}y^{14}}{16x^{8}y^{12}}$$

Cancel out y^{12} in both numerator and denominator.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{y^{2}x^{10}}{16x^{8}}$$

Cancel out x^{8} in both numerator and denominator.

$$\frac{x^{2}y^{2}}{16}$$

Expand

$$\frac{\left(xy\right)^{2}}{16}$$

Solution Steps

Expand \left(\left(-x^{5}\right)y^{7}\right)^{2}.

$$\frac{\left(-x^{5}\right)^{2}\left(y^{7}\right)^{2}}{\left(2x^{2}y^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{\left(-x^{5}\right)^{2}y^{14}}{\left(2x^{2}y^{3}\right)^{4}}$$

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

$$\frac{\left(x^{5}\right)^{2}y^{14}}{\left(2x^{2}y^{3}\right)^{4}}$$

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

$$\frac{\left(x^{5}\right)^{2}y^{14}}{2^{4}\left(x^{2}\right)^{4}\left(y^{3}\right)^{4}}$$

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

$$\frac{\left(x^{5}\right)^{2}y^{14}}{2^{4}x^{8}\left(y^{3}\right)^{4}}$$

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

$$\frac{\left(x^{5}\right)^{2}y^{14}}{2^{4}x^{8}y^{12}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(x^{5}\right)^{2}y^{14}}{16x^{8}y^{12}}$$

Cancel out y^{12} in both numerator and denominator.

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{y^{2}x^{10}}{16x^{8}}$$

Cancel out x^{8} in both numerator and denominator.

$$\frac{x^{2}y^{2}}{16}$$