I’m doing my GED and passed that math part but this never came up. I saw it on a meme and am lost.
Help!!??
In: 9770
My phone says 2 to the zeroth power is 2, no matter how I twig it.
Did I just find a glitch or something?
Everyone is coming up with these more elaborate explanations because they’re starting with the premise that 2^3 is best interpreted as “multiply 3 twos together”.
A description of exponentiation (by integer powers is) that naturally extends to zero is, “Start with 1. Multiply it by the number on the bottom, repeating that process by the number on the top times”. So:
2^4 = 1 × 2 × 2 × 2 × 2 (Multiply 1 by 2 four times.)
2^3 = 1 × 2 × 2 × 2 (Multiply 1 by 2 three times.)
2^2 = 1 × 2 × 2 (Multiply 1 by 2 two times.)
2^1 = 1 × 2 (Multiply 1 by 2 once.)
2^0 = 1 (Multiply 1 by 2 zero times.)
Anything to the power of 0 is 1 by definition. We decided to do that because it makes it consistent with all the properties of exponentiation.
For example,
x^(a-b) = x^a / x^b, so if a=b, then x^(a-a) = x^a / x^a, so x^0 = 1
We took it further, and also defined the operation for negative numbers, so x^(-n) = 1/x^n, because x^(-n) * x^n should equal x^(-n+n) = x^0 = 1.
We have similar definitions for rational numbers, etc. So even though the basic definition is multiply a number n times, we can generalize it in ways that make sense.
Power of 0 of any number being equal to 1 is just a CONVENTION, to make math consistent.
That’s all it is to be for ELI5. Higher knowledge of limits, calculus is required for deeper understanding.
PS: Except 0^(0), that is undetermined.
2^3 is 2x2x2
2^2 is 2×2
2^1 is 2
2^0 is 2/2
2^-1 is 1/2
2^-2 is 1/(2×2)
2^-3 is 1/(2x2x2)
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