Why is zero raise to zero undefined?

Answer 1

By definitions,x^0 = 1 for any non-zero number x

also

0^x = 0 for any positive x

So, if 0^0 was defined, then the first definition would say it was equal to 1 and the second that it was equal to 0.

There is a more detailed but complicated explanation which relies on limits but I hope this will suffice.

Answer 2

There is the following contradiction: if you raise zero to any power, you get zero; if you raise any number to the power zero, you get one.