What is 0 to the power of 0?
In most cases it is reasonable to define it to be 1. In some contexts it may be 0 or undefined. The famous mathematician and computer scientist Donald Knuth explains in one of his books that 0^0 can be seen as special case – of x^0 (in which case it should be 1, because x^0 = 1 holds already for all other x) – of 0^x (in which case it should be 0, because 0^x=0 is true for all x>0) But he then points out that the function x^0 appears quite often in mathematics, for example in the Binomial Theorem, whereas the function 0^x is utterly unimportant. Therefore 0^0 should be seen as a special case of x^0, and hence it makes sense to set 0^0=1.
