0^{x} is unambiguously equal to zero everywhere except at x=0. It may seem odd then to define 0^{0} as one since that makes 0^{x} discontinuous but looking at the function y^x as y approaches zero one sees that such a discontinuous function is exactly what should be expected. This can be clearly seen in the image below. The four lines are 0.1^{x}, 0.01^{x}, 0.001^{x}, and 0.0001^{x}.

## See also

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