Anything multiplied by 0 is 0 right so why does x number raised to the power of 0 = 1? isnt it x^0 = x*0 (im turning grade 10 and i asked my teacher about this he told me its because its just what he was taught 💀)
In: Mathematics
The pure mathematician will tell you: It analytically respects the property *a*^(*x*+*y*) = *a*^(*x*) × *a*^(*y*) that holds true when *x* and *y* are positive integers. It is by extrapolation of this property over all other numbers that we get things such as *a*^0 = 1 for all *a* except 0, *a*^(−*x*) = 1÷*a*^(*x*), *a*^(½) = √*a*, and e^(iπ) = −1.
3Blue1Brown (Grant Sanderson) has a video that tackles this question head-on with an appeal to group theory: https://youtu.be/mvmuCPvRoWQ
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