32 or 64 bit is to do with the length of instructions that the processor can handle, not the maximum numbers it can calculate. Doing 2 ^ 65 is the same as doing:
2*2*2*2*2*2... 65 times. That is just basic maths which is what the CPU is designed to do. You can do that calculations on a pocket calculator. It will give the correct answer, though probably in standard form due to the screen size being too small to show all of the digits, but it is capable.