(x^-2y^2z)^-3/(x^-4y^2z)^-2

(x^-4 y^2 z)^2 / (x^-2 y^2 z)^3

x^-8 y^4 z^2 / (x^-6 y^6 z^3)

x^-2 y^-2 z^-1
or
1/(x^2 y^2 z)