"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?