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Google says the answer is $1$.
Wolfram Alpha says it's undefined.

I saw an argument made for $0^0$ being $1$, on Quora, along the lines of: if you want the binomial theorem to work for real numbers (in the form $(a + 0)^n$ where $a \in \mathbb{R}$), then you should accept that $0^0 = 1.$

Tobi Alafin
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  • https://fr.scribd.com/doc/14709220/Zero-puissance-zero-Zero-to-the-Zero-th-Power – JJacquelin Sep 16 '17 at 15:04
  • If you can't read French, here's an explanation in English: http://oeis.org/wiki/The_special_case_of_zero_to_the_zeroeth_power It includes a few graphs, like $0^x$ and $x^0$, which you might find enlightening. – Robert Soupe Sep 16 '17 at 19:38

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