Why does 0 raised to 0 is not equal to 1?

You have two conflicting rules here: x^0=1 for any x, but 0^x=0 for any x. This means that 0^0 should, by all rights, be 0 and 1 at the same time, if it were defined. For this reason, most people say that 0^0 is undefined. However, people do usually say 0^0=1 if they absolutely have to assign a value to it.