how much does this equal 0^0=?????

Question

0^0=????

Answer 1

This is a special case that's called "indetermined" or "indeterminate form", as is also 0/0.

It IS NOT equal to 1.

It is NOT equal to 0.

And it IS NOT called "undefined" (as is 1/0).

Again, it is called "indetermined". Technically, 0^0 should be the same as 0/0 because 0^0 = 0^(1-1) = (0^1) / (0^1) = (0/0)^1 = 0/0. But 0/0 is indetermined beacuse you can make it take on any value (again, ignoring the no-divisibility-by-zero rule). If 0/0 = x, then 0 = x*0, which means x can be anything.

In SOME cases, you can treat 0^0 as "1". For example, if you're using binomial expansion, then you treat 0^0 as 1 just as you treat 0! = 1. But other than formulas like that where you treat n=0 as an exception ot the rule, we can't say that 0^0 in and of itself has a particular value.

Answer 2

I don't think that the result is so obvious. If you consider that
0^(1/2) = 0, then 0^(1/4) = 0, 0^(1/8) = 0, etc then this suggests that limit(n approaches infinity) of 0^(1/n) = 0 and of course limit(1/n) = 0. This rather suggests that 0^0 = 0 but I must admit that I'm not sure. It's certainly true that funny things happen when you start playing around with 0 and infinity.

Answer 3

1 as n^0=1

Answer 4

It is an indeterminate form. Depending on your function, it may have several values.

WARNING: You must be familiar with the concept of limits to understand the following.

1)f(x)=x^x
lim as x goes to 0 will give us f(0)=1

2)f(x)=0^x
lim as x goes to 0 will give us f(0)=0

So, depending on how you approach 0^0, you will get different limit values. This is why there is no single value equal to 0^0 and this is why 0^0 is an indeterminate form.

Answer 5

0^0 in plain language means "nothing raised to the power of nothing". The commonsense answer therefore should be "nothing" or 0. However, 0 and infinity are concepts in maths that can take on definitions not in tune with "commonsense", as for example 0! = 1 (by definition), (infinity)^0 = indeterminate, inf/inf = indeterminate etc.

Answer 6

n^0=1 (i)
BUT 0^n=0 (ii)

and in any case u need to consider rule (i) first and thus 0^0=1

also, this number is not indetermined or in other words infinite, as in the case of n/0

Answer 7

0^0=1

any number raised to the 0 power=1. even 0.

Answer 8

Your first few answers are silly.

Something raised to the zero power means that you have zero numbers of them.

So, zero zeros means you have zero.

0^0 = 0

---edit---

OK, all of you smart guys who game me the thumbs down should answer this other guy's question if you can:

----edit2---

The idea that zero raised to any power should be anything other than zero seems to defy logic, since if you start with nothing, then you should end with nothing.

If you don't believe me, then consider how much interest you will get on a savings account that has no money in it, for example. Or how many crops will you grow if you plant zero seeds. Common sense suggests that you don't get something out of nothing.

Math cannot contradict nature.

I like the answer from "geezerbill" below who said that it is indeterminate. His answer makes sense.

Answer 9

+1 on the indeterminate form.

Two ways of getting to 0^0:

Note lim_x->0_(x^x) = 1.
Note lim_x->+0_(0^x) = 0.

Since 0^0 can't be both 1 and 0, it is indeterminate.

Answer 10

Well, this may not be properly defined, but it has to be 0

0^0 indicates you are multiplying zero, 0 times. So, the answer should be 0.