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Anything raised to the zero power will equal 1. True False

Mathematics
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  • hba
@SWAG According to exponential rule, \[n^0=1\]

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Other answers:

its trueeeee
what is \[0^0\]?
But\[0^0 = Undefined\]
so that makes it true?
yes ofcourse
@swag - do you know the following rule:\[\frac{x^a}{x^b}=x^{a-b}\]
No
  • hba
I think all the mods are in house today :D
Foreal iv never had so many people or moderators on my question before
Technically, most of the time \(0^0\) is regarded as undefined, but some mathematicians implement the idea that \(0^0=1\) when the feel that it "makes more sense" so to speak.
it's a subtle issue really
take a simple case:\[\frac{x^4}{x^3}=\frac{x\times x\times x\times x}{x\times x\times x}=x\]agreed?
\[\Large \infty^0=?\]
well, you can say infinity is not a number, but still...
Right
who are you responding to there?
it does not a number, it says anything (:
  • hba
Yeah :D
I think @asnaseer originally showed me this: http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/#b
ok, so you should be able to see now that:\[\frac{x^4}{x^3}=x^{4-3}=x^1=x\]
this is where the rule comes from. so, taking the rule:\[\frac{x^a}{x^b}=x^{a-b}\]if you let b=a, you get:\[\frac{x^a}{x^a}=x^{a-a}=x^0\]but:\[\frac{x^a}{x^a}=1\]therefore:\[x^0=1\]apart from the case where x=0
\[\Large N^0=1\]and \[ \Large 0^N=0\]but \[\Large 0^0=0 \] or \[\Large 0^0= 1 \]?
Anything raised to the zero power will equal 1. <---So this would be False, since not EVERY number follows this rule.
  • hba
No it's debatable
if you look at the link @TuringTest posted above, it states under the section "The following is a list of reasons why 0^0 should be 1." some reasons as to why we generally regard \(0^0=1\)
Okay according to my notes in Algebra...it'd be true. I prefer going with what the lesson says. (;
here's another good rundown of the trickyness in finding a direct answer http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/
  • hba
I think so that the answer is TRUE.

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