Question

What is 0^0 equals to?
a.1
b.0
c.undefine

Answer 1

It is defined as zero.

Answer 2

but my calculator says 1 and isn't all numbers raised to zero is equal to 1?
Help! It's very confusing...

Answer 3

Get a new calculator. O to any power is zero, by definition. Technically, O^0 is undefined, because the term x^y as a function of two variables is undefined at the origin.

Answer 4

0^0 is undefined

reason:
0^n = 0 for any value of n
but a^0 = 1 for any value of a
so we have a contradiction, which drives mathematicians crazy, thus it is undefined

my 25 year old calculator gives me an error message for 0^0

Answer 5

However, if you look at the graph for

y = x^x

the limit near zero is 1.

limit x^x
log(limit) = x*logx
= logx/(1/x)
use l'Hospital's rule:
= (1/x) / (-1/x^2)
= -x
log(limit)=0, so limit=1

Answer 6

My two year old calculator gives an answer of "invalid".

Answer 7

thanks for your answers...
I can now explain the different answers to my professor..