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Isn't the logic something like:
4^(1)==4^(4-3)==(4 * 4 * 4 * 4)/(4 * 4 * 4) http://www.wolframalpha.com/input/?i=4^%281%29%3D%3D4^%284-3...
Therefore 4^0==4^(n-n)== ( 4 * 4 * .. * 4 / 4 * 4 * .. * 4 ) ==1 http://www.wolframalpha.com/input/?i=4^0%3D%3D4^%28n-n%29%3D...
So with 0 you would have 0^0==0^(n-n)==(0 * 0 * .. * 0)/(0 * 0 * .. * 0)==0/0==DNE http://www.wolframalpha.com/input/?i=prod%280%2C+for+i%3D0+t...
Of course I use 4 here to be descriptive but it would be equivalent for any nonzero real number.