Why is `9(28^0) =9?`Thought 0 power was that number

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degeneratecircle | High School Teacher | (Level 2) Associate Educator

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Any nonzero number raised to the zeroth power is 1, so `28^0=1.` This is a definition and it's made so that certain patterns hold and the laws of positive exponents carry over to zero and negative exponents.

Consider this:



`28^1=28=784/28`, so the pattern suggests defining


Another way to view it:

For positive exponents, `x^m/x^n=x^(m-n).` Using this we get

`1=28^1/28^1=28^(1-1)=28^0.` Again, this suggests that we should define `28^0` to be 1. This same reasoning can be used to define negative exponents in a consistent way.

Back to the original problem, we have `9(28^0)=9(1)=9.`


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