Ok, i just want someone to explain to me this

10^0 = 1

To me that sounds mathematicly incorrect. Presumably we know that 10^2 = 100 because that is saying that you have to lots of 10 and you are multyplying them together. Therefore 10^3 means you have 3 lots of ten and you are multyplying them all together, which it does. Therefore 10^0 means you have 0 lots of ten and you are multyplying them together. Therefore the answer should be 0? correct

Or is there something i'm missing here?!

thanks
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Anything to the 0 is 1

1^0=1
5^0=1
24365249^0=1

Don't question it man, just accept it
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10^3 = 1000
10^2 = 100
10^1 = 10

10^-1 = 1/10
10^-2 = 1/100
etc...

10^0 = 1 fits the pattern, am I correct?
Well, if you're going to use ten as an example:

To find the power of ten, you just take the exponent and put that many zeros behind a one. An exponent of 0 would mean you have no zeros to put behind it, so it's just one.

However, mathematically it has something to do with properties of multiplication and such.

edit: Here, Wikipedia has a good mathematical explanation.
x^n*x^y=x^(x+y)

x^n*x^n=x^2n

x^n/x^n=x^0=1

If you can follow it, that should explain it
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I cant rember why but their is a perfectly good explanation to why anything to the power of 0 = 1
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Anything to the 0 is 1
Don't question it man, just accept it

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Imagine it better like:

10^-2 = 0.01
10^-1=0.1
10^0= ....
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Ok i get it now, thanks to the guy with the wikipedia link, it wasn't taught nething like that today!! but now it's clear, cheers guys!
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When we were shown it by our teacher we were shown;

x^y / x^z = x^(y-z) [just the straight forward "dividing indices" rule]

If y = z

x^y/x^z = x^0

A number divided by itself is 1. y = z, hence x^y = x^z.

Therefore x^y/x^z = 1.

And so x^0 = 1.

I know you said you get it now, but I just thought I'd share my way of proving it.
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Quote by chubbychunks
10^3 = 1000
10^2 = 100
10^1 = 10

10^-1 = 1/10
10^-2 = 1/100
etc...

10^0 = 1 fits the pattern, am I correct?

Yes.

The way my math teacher explained it, it exists that way simply because it has to.
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I never actually bothered thinking about why x^0 = 1 before now, I was told it years ago and told it just did, so that's all I've thought of it as.

If you think that's odd, wait until later when you get told e^pi(i) + 1 = 0 where i = the square root of (-1).
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anything to the 0 power is one!
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I cant rember why but their is a perfectly good explanation to why anything to the power of 0 = 1

Haha. Yes we all know there is, james. We all know there is.
Because it's base ten. All numbers can be explained in terms of their base number system...thats where we get "place values" from.
The 1's place
10^0 = 1

The 10's place
10^1 = 10

...and so on.

Now you just multiply whatever number occupies that place so the number 3, is actually 3X10^0

Binary works the same way but in base 2.
2^0 = 1
2^1 = 2
2^2 = 4
a/a=1

a^x/a^x=a^0=1

it's perfectly understandable

if you're talking about why it's not 0 when the "power" is 0 you just have to remember that exponents are always positive.. they're never even 0

pretty simple in my opinion
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x^n / x^m = x^(n-m), right? So then
x^4 / x^4 = x^(4-4), and 4-4 = 0. But we know that any number (in this case x^4) divided by itself equals one, so:

x^4 / x^4 = x^0
x^4 / x^4 = 1
x^0 = 1

if you're talking about why it's not 0 when the "power" is 0 you just have to remember that exponents are always positive.. they're never even 0

Exponents can be negative...

x^(-n) = 1 / x^n
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Last edited by Raziel2p at Oct 19, 2007,
10^0=(1*10/1*10)=1/1=1
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