T^m

For an operator T \in \mathcal{L}(V), T^{n} would make sense. Instead of writing TTT\dots, then, we just write T^{n}.
constituents operator T \in \mathcal{L}(V) requirements T^{m} = T \dots T additional information T^{0} \begin{equation} T^{0} := I \in \mathcal{L}(V) \end{equation}
T^{-1} \begin{equation} T^{-m} = (T^{-1})^{m} \end{equation}
if T is invertable
usual rules of squaring \begin{equation} \begin{cases} T^{m}T^{n} = T^{m+n} \ (T^{m})^{n} = T^{mn} \end{cases} \end{equation}
This can be shown by counting the number of times T is repeated by writing each T^{m} out.