I usually avoid x^y because it is used in programming to indicate a bitwise XOR. The double-star operator isn’t often used for anything except exponents though.
HTML allows showing powers as superscripts, like xy, but that also doesn’t work in programming languages… and neither do the unicode characters for raised numbers. So I try to stick to just 7-bit ascii whenever possible. It works pretty much everywhere, on any system built after 1970.