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
>where a formula would apply. This always helps, but i can’t find one here.
When dividing two numbers, you can express them as exponents and subtract the exponents.
e.g. 8 / 4 = 2
But we could say
2^3 / 2^2 = 2^1
The general formula is: x^a / x^b = x^(a-b)
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A number divided by itself equals 1.
x / x = 1 (for x not equal to 0).
Well, if that is true, then we can pick any (non-zero) number we want.
Instead of just “x” let’s try some power of x. Let’s use x^n, where n is just some (non-zero) number.
x^n / x^n = 1.
But, from the previous formula for dividing exponentials:
x^n / x^n = x^(n-n)
So x^n/x^n equals two things, and so those two things must also be equal.
Therefore x^(n-n) = 1
But we can simplify “n-n” to 0.
So x^0 = 1.
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