Question

anyone can tell my why a^0=1
am gone to crazy
pliz help!!??

Answer 1

a^1=a
divide by a:
a^(1-1)=a^0=a/a=1

Answer 2

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.

Answer 3

ONLY if\[ a\neq0\]if \(a=0\), we have a controversy

Answer 4

ammm

Answer 5

true: consider http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

Answer 6

yeah... @turingtest is right... one sore EXCEPTION!! aryabhatta's "0" :p :p :D

Answer 7

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

Answer 8

last line is supposed to be\[\implies a^0=\frac aa=0\]

Answer 9

\[\implies a^0=\frac aa=1\]

;)

Answer 10

yeah something like that :P

Answer 11

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 \(a^0=1\)

Answer 12

no, I'm afraid you completely missed the point
nothing here suggests that 0^0=1

Answer 13

ammmmmmmmm

Answer 14

\[0^0\] is usually undefined

Answer 15

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)

Answer 16

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

Answer 17

thanks (turing test) for your Interest

Answer 18

likewise