Solve x^-2+y^-2/(xy)^-2

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

Evaluate

$$x^{2}+y^{2}$$

Short Solution Steps

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

$$\frac{x^{-2}+y^{-2}}{x^{-2}y^{-2}}$$

Factor the expressions that are not already factored.

$$\frac{\left(y^{-2}x^{2}+1\right)x^{-2}}{x^{-2}y^{-2}}$$

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

$$\frac{y^{-2}x^{2}+1}{y^{-2}}$$

Expand the expression.

$$\frac{1+\left(\frac{1}{y}x\right)^{2}}{y^{-2}}$$

Express \frac{1}{y}x as a single fraction.

$$\frac{1+\left(\frac{x}{y}\right)^{2}}{y^{-2}}$$

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

$$\frac{1+\frac{x^{2}}{y^{2}}}{y^{-2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{y^{2}}{y^{2}}+\frac{x^{2}}{y^{2}}}{y^{-2}}$$

Since \frac{y^{2}}{y^{2}} and \frac{x^{2}}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{2}+x^{2}}{y^{2}}}{y^{-2}}$$

Express \frac{\frac{y^{2}+x^{2}}{y^{2}}}{y^{-2}} as a single fraction.

$$\frac{y^{2}+x^{2}}{y^{2}y^{-2}}$$

Multiply y^{2} and y^{-2} to get 1.

$$\frac{y^{2}+x^{2}}{1}$$

Anything divided by one gives itself.

$$y^{2}+x^{2}$$

Expand

$$x^{2}+y^{2}$$

Short Solution Steps

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

$$\frac{x^{-2}+y^{-2}}{x^{-2}y^{-2}}$$

Factor the expressions that are not already factored.

$$\frac{\left(y^{-2}x^{2}+1\right)x^{-2}}{x^{-2}y^{-2}}$$

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

$$\frac{y^{-2}x^{2}+1}{y^{-2}}$$

Expand the expression.

$$\frac{1+\left(\frac{1}{y}x\right)^{2}}{y^{-2}}$$

Express \frac{1}{y}x as a single fraction.

$$\frac{1+\left(\frac{x}{y}\right)^{2}}{y^{-2}}$$

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

$$\frac{1+\frac{x^{2}}{y^{2}}}{y^{-2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y^{2}}{y^{2}}.

$$\frac{\frac{y^{2}}{y^{2}}+\frac{x^{2}}{y^{2}}}{y^{-2}}$$

Since \frac{y^{2}}{y^{2}} and \frac{x^{2}}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{2}+x^{2}}{y^{2}}}{y^{-2}}$$

Express \frac{\frac{y^{2}+x^{2}}{y^{2}}}{y^{-2}} as a single fraction.

$$\frac{y^{2}+x^{2}}{y^{2}y^{-2}}$$

Multiply y^{2} and y^{-2} to get 1.

$$\frac{y^{2}+x^{2}}{1}$$

Anything divided by one gives itself.

$$y^{2}+x^{2}$$