X² is X times X.
X¹ is X.
In X^Y Y is the factor that decides how many Xs are getting multiplied.
So why is X⁰ 1? It comes out of nowhere. Zero Xs are getting multiplied, so there’s no numbers being multiplied, meaning there’s nothing.
In: Mathematics
The jump from multiplication to exponentiation is more complicated than it is first taught in school.
Some examples where the multiplication analogy falls apart include:
X^(½) is the same thing as the square root of X. If you choose X = 4, then X^(½) = 2.
X^(-1) is the same thing as 1/X. If you choose X = 4, then X^(-1) = ¼
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However, you can make the multiplication analogy work for X^0 because 1 is the multiplicative identity (1 * X = X for any X). Therefore, this is a valid interpretation:
X^2 = 1 * X * X
X^1 = 1 * X
X^0 = 1
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