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

Here’s my intuitive way of understanding it.

10^(1) = 10

10^(2) = 100

10^(3) = 1,000

etc. The pattern you see is that the number of zeros in the value resulting from raising 10 to some exponent is whatever number that exponent is. So

10^(0) = 1 (zero 0’s).

See, the thing is, I didn’t say what number base I was using; we all presumed this was base 10, but technically speaking, this example could have been base 4 or higher based on the numerals I used. This works for any number base. And since it works for any number base, if you just write that in base ten, then you can put any number for x, and

x^(0) = 0

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