When we define a structure, let's say a group, we write $(G ,\oplus )$ for an operation $\oplus$. In case I want to define a structure with operation exponentiation I just define the $\oplus$ so that $a \oplus b = a^b$, which is what I have done until now. But a curiosity of mine is, if there exists, or if it ever existed, a symbolic representation of exponentiation.
Thus, have you ever come across a symbol for exponentiation?
Generally the caret ( ^ ) symbol and (as Yves mentioned) the up arrow ( ↑ ) is used for exponentation.