I dunno why, but today I realized I had a problem accepting that x^{0}=1. (Maybe I'm just saying it wrong in my head, but something multiplying by itself zero times, and that equaling 1 doesn't click with me.) So I came home and looked up the proofs for it, the best so far involves that rule of exponents.

This makes total sense to me:

5^3 / 5^2 = 125 / 25 = 5

5^3 / 5^2 = 5 ^(3-2) = 5^1 = 5

5^3 / 5^3 = 125 / 125 = 1

5^3 / 5^3 = 5 ^(3-3) = 5^0 =

... and the result must be 1. So 5^0 =1.

But I can't help but wonder whether we're expressing it wrong.

Is there any sort of proof verifying that x^b / x^c = x^(b-c)? I'm sure there is, but typing that into Google gave me random weird things, and I'd like to see it for myself.

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## Izzy 1

I dunno why, but today I realized I had a problem accepting that x

^{0}=1. (Maybe I'm just saying it wrong in my head, but something multiplying by itself zero times, and that equaling 1 doesn't click with me.) So I came home and looked up the proofs for it, the best so far involves that rule of exponents.This makes total sense to me:

5^3 / 5^2 = 125 / 25 = 5

5^3 / 5^2 = 5 ^(3-2) = 5^1 = 5

5^3 / 5^3 = 125 / 125 = 1

5^3 / 5^3 = 5 ^(3-3) = 5^0 =

... and the result must be 1. So 5^0 =1.

But I can't help but wonder whether we're expressing it wrong.

Is there any sort of proof verifying that x^b / x^c = x^(b-c)? I'm sure there is, but typing that into Google gave me random weird things, and I'd like to see it for myself.

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