What is the value of 0^0?

Answer 1

Undefined!

Answer 2

1

Answer 3

1

Answer 4

1

Answer 5

0^0=1

Answer 6

1

Answer 7

1

Answer 8

Munir B is on the right track in recomending the use of calculus, but the answer isn't entirely correct.

0^0 is what's termed an 'indeterminate form', along with things like 0/0, inf/inf and 1^inf (where inf indicates infinity).

In this case, you can attempt to evaluate the exact value of the expression using limits - the first logical step would be to replace the base in the expression with some variable, like so: x^0.

Next, you would evaluate the limit as x->0 - if you don't have any calculus knowledge, this basicly means that you're going to examine the values of the expression for some number 'x', and let 'x' get closer and closer to zero, without actually reaching it. This method allows you to see what will happen to the expression when the value actually DOES reach zero.

There's a little bit more math involved, but it can be proven that 0^0 can indeed equal ANY value between 0 and 1 - as a result, this is a true indeterminate form. Since we can't determine what it equals one way or another, we can't really use it for anything useful (in general).

There are ways of dealing with these, however. There was a French guy by the name of L'hopital who invented a rule for evaluating inteterminate forms that arise from various calculus problems. In this case, the general proccess would be to use the natural logarithm and the number 'e' to reduce the expression to some rational function (that is, some thing divided by something else), and then take the derivative of the function on top of your division sign and the derivative of the function on the bottom of the division sign, and then evaluate the limit of the result. In this case, you'll also need to 'work backwards' after you have a result, in order to eliminate the mess that you've created with the natural log.

The details of this are usualy taught in a second semester calculus course, or towards the end of the first semester. The rules for Logarithms and exponential functions are generaly introduced in a college algebra course or a high school 'advanced algebra' course.

Answer 9

Depends where the zeros came from. For example, 0^0 is undefined, but the limit of x^0 when x approaches 0 is 1, while the limit of 0^x when x approaches 0 is 0.
I hope this is confusing enough.

Answer 10

0^0 is undefined. There are lots of reasons as to why.

For example:
Consider the function f(x) = x^0. For nonzero x, f(x) = 1. Thus
lim_{x -> 0} f(x) = 1.
On the other hand, let g(x) = 0^x. For positive x, g(x) = 0. Thus lim_{x -> 0+} g(x) = 0.

As away from zero, these are both continuous functions, the only way we can keep them continuous is to have 0^0 undefined.

Answer 11

It is Undefined Period. Regardless of the fact that 0^X is 0 for any X and X^0 is 1 for any X. These two rules obviously conflict in the case of 0^0 therefore the expression is undefined.