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What is 0 ^ 0

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Answer

Indeterminate

Explanction
If you take a sequence

     1.0   0.5   0.25
    0,  , 0   , 0   , ...  etc

You will get 0 for all values.

Now consider the sequence

      0    0    0     0     
     1, 1.0, 0.5, 0.25, ... etc

You will get 1 for every positive base. So you think 0^0 would also be 1.

So the final result will be that you can get any value between 0 and 1. This value will not be a fix number. And something that can not express as number is said to be indeterminate.

Now look at the following expression 
         (1/n)
    (x^n)  

As n-> ∞, this fraction goes to 0^0, but if it is just x the whole time, the limit of the expression as it goes to 0^0 is x.
So we could make it anything in between 0 and 1. So it is indeterminate.

Indeterminate means something that has no definite value. Something that cannot be expressed as a NUMBER.

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Undefined, Indeterminate

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