why is x to the power of 0 always 1?

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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.

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Anonymous 0 Comments

>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)

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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