(x^{2 }y^{2 })^{-1}

A negative exponent means that the information in parenthesis should be moved to the other side of the fraction (from numerator to denominator or from denominator to numerator).

Since x^{2}y^{2} is being taken to the -1 power, both the x^{2} term and the y^{2} term should be moved to the denominator.

The answer is:

1/(x^{2}y^{2})