"I don't think this is what you mean, is it?"

If $X$ and $Y$ are sets, the set of functions from $X$ to $Y$ \(often written $X \\to Y$\) is sometimes also written $Y^X$\. This latter notation, which I'll call exponential notation, is related to the notation for finite powers of sets \(e\.g\., $Y^2$ for the powers of triples of elements of $Y$\) as well as the notation of exponentiation for numbers\.

I don't think this is what you mean, is it?