Solve (frac{x^{2}y^20}{x^6y^15})^2

$$( \frac { x ^ { 2 } y ^ { 20 } } { x ^ { 6 } y ^ { 15 } } ) ^ { 2 }$$

Evaluate

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

Solution Steps

Cancel out x^{2}y^{15} in both numerator and denominator.

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

To raise \frac{y^{5}}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{y^{10}}{\left(x^{4}\right)^{2}}$$

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

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

Expand

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

Solution Steps

Cancel out x^{2}y^{15} in both numerator and denominator.

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

To raise \frac{y^{5}}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{y^{10}}{\left(x^{4}\right)^{2}}$$

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

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