What is 00? And I'm not expecting some miracle answer or nothing, I'm expecting the truth. And actually, it's much more complex than you might think (and I'm not talking about i here).
My point is, powers with base 0 (0n) could be forbidden.
It is known that xm*xn=x(m+n).
But also that xm/xn=x(m-n).
So if you might call 02 as 0, or 03, you would be forced to say 03/02, that is 01, would be 0/0.
But there is something wrong about that.
Remember when we talked about 0/0? It could even be 0!
But we know that when we say 01, we're talking about a number that when you multiply 1 zero together (that is, leave it as it was), you're talking about 0! So 0/0 is 0 in this case.
But 00 has nothing to forbid it.
The only reason mathematicians called n0 as 1, was because n1 =(n)/n1, (that is n(1-1)=n0) was always 1... except for 0.
So the only thing that can define without barriers 0^0 is... Our number with infinite answers! 0/0! (or 0j, if you remember one of our last episodes)! But of course because almost everyone else believes 0/0 is undefined, 00 is as undefined as.
-The Roaring Thunder