Thread: 0^0 = 1? View Single Post
 Quote by CRGreathouse I don't think that it's undefined; I think that it's 1. 0^0 is an empty product, and empty products are necessarily equal to 1. As Galileo points out above, we need 0^0=1 for series to have compact formulas. Everyone agrees that $$x^0=1$$ for $$x\neq0$$, but there's no reason to think that it should be different at 0 -- $$0^x$$ is only 0 for x > 0, since it's not defined for negative x. There's no problem accepting 0^0 as 1, and there are many good reasons to think it shouldn't be undefined or 0.
$$x^0 = \frac{x}{x}$$.