If $G$ is a group and we have subsets $S,T\subseteq G$, then we define the product of these subsets as $$ST=\{st; s\in S, t\in T\}.$$ (Maybe for abelian groups and additive notation the name sum is also used.)
When dealing with groups, the set $U^2=UU$ and $U^{-1}=\{u^{-1}; u\in U\}$ are often used. More generally, we can also define $U^n$ for any integer $n$. (Here $U\subseteq G$ can be any subset of $G$. Maybe they are encountered even more often when dealing with topological groups and $U$ is a neighborhood of the identity.)
Question. Is there a commonly used name for $U^2$ and $U^{-1}$? And perhaps also for $U^n$?
I would guess inverse of $U$ for $U^{-1}$. But I am not sure whether somethings like $U$ squared or $n$-th power of $U$ is used for $U^2$ and $U^n$.