For integers, the only exponentiation operations that are normally present in hardware are the shifts,
>> (in C parlance), which multiply by exponential powers of two. For anything else with integers, you run out of bits to represent things far too quickly for it to be useful; by the time you've sorted that problem out, you might as well not have special hardware support as you've also had to deal with memory management and other such expensive things.
I don't know floating-point hardware so well, but hardware exponentiation makes more sense there as you've got the numeric range to make it reasonable. (My google-fu indicates that someone seems to be selling the hardware layout to make this possible…)