Solve (frac{x^{-5}y^2}{x^2y^6})^2

$$( \frac { x ^ { - 5 } y ^ { 2 } } { x ^ { 2 } y ^ { 6 } } ) ^ { 2 }$$

Evaluate

$$\frac{1}{y^{8}x^{14}}$$

Solution Steps

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

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{y^{4}x^{7}}\right)^{2}$$

To raise \frac{1}{y^{4}x^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{2}}{\left(y^{4}x^{7}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\left(y^{4}x^{7}\right)^{2}}$$

Expand \left(y^{4}x^{7}\right)^{2}.

$$\frac{1}{\left(y^{4}\right)^{2}\left(x^{7}\right)^{2}}$$

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

$$\frac{1}{y^{8}\left(x^{7}\right)^{2}}$$

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

$$\frac{1}{y^{8}x^{14}}$$

Expand

$$\frac{1}{y^{8}x^{14}}$$

Solution Steps

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

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{y^{4}x^{7}}\right)^{2}$$

To raise \frac{1}{y^{4}x^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{2}}{\left(y^{4}x^{7}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\left(y^{4}x^{7}\right)^{2}}$$

Expand \left(y^{4}x^{7}\right)^{2}.

$$\frac{1}{\left(y^{4}\right)^{2}\left(x^{7}\right)^{2}}$$

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

$$\frac{1}{y^{8}\left(x^{7}\right)^{2}}$$

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

$$\frac{1}{y^{8}x^{14}}$$