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Zero to the Zero Power. It is commonly taught that any number to the zero power is 1, and zero to any power is 0. But if that is the case, what is zero to the zero power? Well, it is undefined (since xy as a function of 2 variables is not continuous at the origin). But if it could be defined, what should it be?
Well, if I want to multiply it by 2 zero times, that means I'm just left with the 1. So 2 to the zero power is going to be equal to 1. And, actually, any non-zero number to the 0 power is 1 by that same rationale. And I'll make another video that will also give a little bit more intuition on there. That might seem very counterintuitive, but it's based on one way of thinking about it is thinking of an exponent as this.