Solve x^-2/y^2*(1/xy)^-2

$$\frac { x ^ { - 2 } } { y ^ { 2 } } \cdot ( \frac { 1 } { x y } ) ^ { - 2 }$$

Evaluate

$$1$$

Solution Steps

To raise \frac{1}{xy} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{x^{-2}}{y^{2}} times \frac{1^{-2}}{\left(xy\right)^{-2}} by multiplying numerator times numerator and denominator times denominator.

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

Calculate 1 to the power of -2 and get 1.

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

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

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

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

$$\frac{x^{-2}\times 1}{x^{-2}}$$

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

$$1$$

Factor

$$1$$