It kinda doesn’t make sense.
x¹= x
x² = x*x
x³= x*x*x
etc…
and even with negative numbers you’re still multiplying the number by itself
like (x)-² = 1/x² = 1/(x*x)
In: 1797
Well, a simple reason is that we want x^a times x^b to be x^(a+b).
So: x^1 is x. x^(-1) is 1/x. What is x times 1/x? It’s 1. But that’s also x^1 times x^(-1) = x^(1 + -1) = x^(0).
A somewhat more formal approach is to think of x^0 as an empty product. You’re not multiplying anything, which is the same as multiplying by 1. Or to extend your logic from the OP:
> It kinda doesn’t make sense
> x*1 = x
> x*2 = x + x
> x*3 = x + x + x
So in this case, x*0 is the empty sum, which is the same as not adding anything, which is the same as adding 0. (And of course, x * 0 is in fact 0.)
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