Evaluate: $$0^0$$
Would you use this law of indices?
$$x^0=1$$
Or would you use that:
$$\frac{x^n}{x^n}=x^0$$ which would mean $$\frac{0}{0}=undefined$$
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Xetrov
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1See also https://math.stackexchange.com/questions/11150/zero-to-the-zero-power-is-00-1?noredirect=1&lq=1 – Arnaud D. May 17 '17 at 15:02
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I'd use $0^0=1$. Makes sense if you consider the function $x\mapsto x^x$ for $x\geq 0$. – Wuestenfux May 17 '17 at 15:08
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This has been asked many times on this site. $0^0$ is undefined without being explicit. Most of the time, it's defined to be equal to $1$ for convenience, such as in the binomial theorem. – Jam May 17 '17 at 15:43