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

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patriciabmcca... | High School Teacher | eNoter

Posted September 25, 2012 at 1:32 PM via web

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Why is `9(28^0) =9?`

Thought 0 power was that number

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

Posted September 25, 2012 at 2:25 PM (Answer #1)

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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:

`28^3=21952`

`28^2=784=21952/28`

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

`28^0=1=28/28.`

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.`

Sources:

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tobimontana | Student, Undergraduate | eNoter

Posted September 25, 2012 at 2:55 PM (Answer #2)

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because ANYTHING raised to the power of zero is 1,and one being in the bracket,9x1=9

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zeze13 | Student, Grade 9 | eNoter

Posted September 25, 2012 at 9:11 PM (Answer #3)

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because any number to the zero power is 1...therefore 9x1=9

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