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

So, the very concept of power in its naive terms is repeated multiplication, right? So, for example, 3⁴ = 3 * 3 * 3 * 3.

When you elevate a number to the power of a sum x^(a+b), what you are basically doing is multiplying the number a times and then multiplying it again b times, which is equivalent to x^a * x^b

This also mean that x⁰ multiplied by x is equal to x^(0+1), which is x¹, which is just x. But if anything multiplied by x is x, then that something is 1. No other number, when multiplied by any number, yields that very number.

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