Hope this post formats okay..

0
x = 1 regardless of the value of x, right?

But:

x
0 = 0 regardless of the value of x.

So, what does that make:

0
0 equal??

My guess would be 1, but I can't be sure..

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Wonder Squirrel

Any number times 0 equals 0. That includes 0. So 0^0=0

Very true.. although..

0 cubed, 0x0x0 = 0
0 squared, 0x0 = 0
0 to the power 1 = 0 - the original number - equivalent to 0x1 if you like.

But, with 0 to the power 0, you're not really multiplying by anything, are you?

I don't disagree with what you've said, it just doesn't explain it too well for me. =)

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Wonder Squirrel

3^0 = 3/3 =1

0^0 =0/0

0 divided by any number is still zero

any number divided by zero is undefined

therefore 0^0 is either 0 or undefined
lets leave that one to the philosophers

Why is anything rised to the zero power one? i asked my math teacher this like 3 years ago, back in algbra, she never gave an answer.

CTR

I think this might explain it:

3^0=3*(1/3)=1

or

x^0=x * (1/x) = 1

Hope that helped

I don't think there's an official answer to this one.....

quote:

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Originally posted by jsaxton14:
I think this might explain it:

3^0=3*(1/3)=1

or

x^0=x * (1/x) = 1

Hope that helped

---

Yeah thats helps, thanks...

CTR

In a case like this the more important rule trumps the lesser one. 0 x 0 = 0 is more important than x^0 = 1.

Any number raised to the 0 power is equal to 1.

You know when you divide numbers raised to exponental powers, if they have the same base number, all you need to do is subtract the exponentals.

Here is the proof:

(10^2)/(10^2) = 100/100 = 1

100 in exponential form is 10^2, since the base number is 10, and they're the same, you can subtract the exponentials. In this case 2-2 = 0 so what is left in the expression is 10^0 or 1.

I just plugged 0^0 in the calculator and it said 1. But that is sort of strange, since you are dividing by 0, the number should be undefined (or in terms of limits: infinity).

Hope this helps.

quote:

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Originally posted by brainuser:
In a case like this the more important rule trumps the lesser one. 0 x 0 = 0 is more important than x^0 = 1.

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But surely 0 x 0 is 0 squared?

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Wonder Squirrel

0 is the exception for a lot of maths rules. If you punch 0^0 into a scientific calculator you'll get "Error 2" or "Unable to calculate"

What about the zero product property wouldn't that mean that 0^0 is 0 ?

and 0/0 isn't undefined?

so .... what's 0^0? 0, 1, undefined???

The four calculators I just tried say 0^0=1. And: http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

Ah, nifty. Thanks for the link xenosss. I guess this kinda means the answer depends on context. And when no context is specified, 0^0=1

Neat.

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Wonder Squirrel

i think there are 1 0's in 0 therefore 0^0=1. But I dont believe it.

zero is not a number and the 0^0 is undefined. Not 0 not 1 simply undefined.

It is just a matter of philosophy.