x * (5**1) = x * 5
x * (0**1) = x * 0 = 0
x * (5**0) = x
x * (0**0) = x
A useful way to think about it is that the exponent is telling you how many times to multiply by something.
If you multiply x by 5 once you get 5x. If you don't multiply it by 5 at all, you just have the x you started with. That's the same as multiplying it by 5 zero times, and the same as multiplying it by 1.
If you don't multiply x by 0 at all, you still have the x you started with. It gives the same as multiplying x by one, so that's why we can say the value of 0**0 is 1.
As bart indicates, 0**0 is a bit of a strange consruct, whith strange relatives, but for simpler operations like the arithmetic most of us normally do in perl, it's really helpful to have it's value be 1, not undefined.
Hope this helps.