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# what is 0 to the power of 0 ??????

i know there is not a definate answer but it will be intresting to hear what you guys think

### 11 Answers

- SuperLv 49 years agoFavorite Answer
Anything to the power of 0 is 1. 0 to the power of anything is 0. So which one dominates? Well, have you tried plotting x^x and going to numbers very close to 0? Go to 10^-6. So what's (10^-6)^(10^-6)? It is close to 1 and it gets closer for smaller values of x. So 0/0 is 1 to an APPROXIMATION. Now don't go around saying that 0 to the power of 0 is 1 cause that's wrong. But you can say that it can be approximated to be 1.

Peace.

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- ?Lv 69 years ago
0 to the power of 0 is not 0. This is an indeterminate form. Don't ever think that 0 to the power of 0 is 0. That isn't true. In calculus you'll have to take limits and from time to time you'll get 0 to the power of 0. To solve problems like these you must take the log of both sides and then take the limit. When you get a number you must put e under it.

- John AdriaanLv 69 years ago
By definition, anything to the power 0 is 1. Therefore 0⁰ = 1 too.

Why? If you have the following:

2x³-6x²+5x¹-3x⁰, then that simplifies to 2x³-6x²+5x-3, because everyone knows that anything to the power 0 is 1.

But what if x=0? If 0⁰ equalled zero, unlike every other value for x, the equation would fail: the 3 would simply disappear. That can't happen, so 0⁰=1 just like every other number.

- 9 years ago
0^0 is the same as

0^1 * 0^-1 based on exponent rules

this becomes

0 * 1/0

which does not exsist because you can't divide be zero