(In reply to Second Computer Solution
If you research the definition of 0^0 you will find that it should be set according to the needs of a specific problem.
Depending on the context where 0^0 occurs, you might wish to substitute it with 1, indeterminate or undefined/nonexistent
One might say that a^0 is 1 for any a , the other will claim that 0^a is zero for any a , but if we consider functions f(x) and g(x) then the limit of f^g when x ==>0 may be any number between 0 and 1; e.g. lim (e^(-1/x))^x equals 1/e if x ==>0.
Since our problem specifies "no zeros" I see no reason to introduce an irrelevant definition of 0^0=0.
Please try Google (several entries) for
Zero to the zero power