(2ab^2)^-2*(a^2b)^2/(3a^3b)^2*(ab^3)^-2

(2ab^2)^-2*(a^2b)^2/(3a^3b)^2*(ab^3)^-2=1/4a^-2b^-4*a^4b^2/(9a^6b^2*a^-2b^-6)=1/4a^2b^-2/(9a^4b^-4)=1/4a^2b^-2*(a^-4b^4)*1/9=1/4*a^-2b^2*1/9=a^-2b^2/36=b^2/(36a^2)