I tried to google a proof, and i found that it comes from the formula: x^1*(1/x^1) where the two x^1s cancel eachother out. I wasn’t satisfied with the answer, so i am still somewhat confused.
Usually when there’s some math i don’t get, i try to imagine a scenario irl, where a formula would apply. This always helps, but i can’t find one here.
In: 5
Leaving aside 0 powers for a moment, what is x^y / x^z ?
Well, let’s look at a few examples.
2^10 / 2^8 = 1024 / 256 = 4 = 2^2 = 2^(10 – 8)
3^3 / 3^1 = 27 / 3 = 9 = 3^2 = 3^(3 – 1)
In general, we find that x^y / x^z = x^(y – z)
So what if z = 0?
Well x^y / x^0 = x^y, therefore x^0 *has* to be 1, regardless of what x is. If it wasn’t, then our rule for dividing powers wouldn’t work.
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