anonymous
  • anonymous
anyone can tell my why a^0=1 am gone to crazy pliz help!!??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
a^1=a divide by a: a^(1-1)=a^0=a/a=1
apoorvk
  • apoorvk
okay simple.... a^2 mean 1*a*a a^3 means 1*a*a*a a^n means 1*a*a*a*......*a ---> (n times) so a^0 means '0' times multiplication of 'a' now a '1' is already there, its just we don't write it. so 1 remains alone!! (i know you will want to know why isn't it 0 then)... and for that matter you can multiply as many 1's as you want, there is no effect.
TuringTest
  • TuringTest
ONLY if\[ a\neq0\]if \(a=0\), we have a controversy

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anonymous
  • anonymous
ammm
anonymous
  • anonymous
true: consider http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
apoorvk
  • apoorvk
yeah... @turingtest is right... one sore EXCEPTION!! aryabhatta's "0" :p :p :D
TuringTest
  • TuringTest
but to provide yet another "proof" of something that is not really true\[a=a^1=a^{1+0}=a\cdot a^0\implies a=\frac aa=0\]notice this "proof" is invalid if a=0, because you cannot divide by zero
TuringTest
  • TuringTest
last line is supposed to be\[\implies a^0=\frac aa=0\]
Zarkon
  • Zarkon
\[\implies a^0=\frac aa=1\] ;)
TuringTest
  • TuringTest
yeah something like that :P
Zarkon
  • Zarkon
I like ...let \[a^0=k,\,\, a\neq 0\] then \[k^2=a^{0}a^{0}=a^{0+0}=a^{0}=k\] so \[k^2=k\] then \[k=0\text{ or }1\] if \(k=0\) then \(0=0\cdot a=a^0\cdot a=a^{0+1}=a\neq 0\). A contadiction..thus \(a^0=1\)
TuringTest
  • TuringTest
no, I'm afraid you completely missed the point nothing here suggests that 0^0=1
anonymous
  • anonymous
ammmmmmmmm
Zarkon
  • Zarkon
\[0^0\] is usually undefined
TuringTest
  • TuringTest
the short answer that I can give you is\(0^0\) is undefined as far as most situations are concerned however quite a number of mathematicians have actually given reason to \(define\) \(0^0=1\) (Euler, for instance)
TuringTest
  • TuringTest
you should perhaps read this for starters, and continue digging if you really want to understand http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/#b
anonymous
  • anonymous
thanks (turing test) for your Interest
TuringTest
  • TuringTest
likewise

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