Perhaps Solve for Subscript[w,s]
Subscript[w,s]=Subscript[w,s]/.Solve[?*Subscript[a,s](Subscript[a,s]Subscript[w,s]^?)^(?-1)==w,Subscript[w,s]][[1]]
and then Simplify for Subscript[m,w]
Simplify[?*Subscript[a,u](Subscript[a,s]Subscript[w,s]^?)^(?-1),0<?<1&&0<?<1&&0<Subscript[a, s]]>Subscript[m,w]