eli5: why is x⁰ = 1 instead of non-existent?

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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

38 Answers

Anonymous 0 Comments

Imagine, instead of it being just X, X^(1) is actually X/1. If you multiply by any value equivalent to one, the original value remains unchanged, so multiplying by 1/1 is perfectly fine, the main purpose is that I want to *express* positive powers of X by X^(y) /1. If you have one x, it’s just one on the top. X^(2) same just with two, etc. Why I’m doing this will be clear momentarily.

So with negative powers, X^(-y) for instance, it’s instead 1/X^(y). For every negative power you go, there’s another x multiplied by the on the *bottom* this time. So for positive powers of X they go on the top, and for negative they go on the bottom.

What happens if you have no X’s in either direction, positive or negative? Nothing on the top, nothing on the bottom, you get 1!

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