#1
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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#2
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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#3
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?
#4
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.
#5
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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#6
I cant rember why but their is a perfectly good explanation to why anything to the power of 0 = 1
#7
Quote by whatamidoinhere
Anything to the 0 is 1
Don't question it man, just accept it


+1
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#8
Imagine it better like:

10^-2 = 0.01
10^-1=0.1
10^0= ....
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#10
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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#11
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.


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#12
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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#13
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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#14
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#15
anything to the 0 power is one!
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#16
Quote by james05090
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.
#17
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
#18
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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#19
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,
#20
10^0=(1*10/1*10)=1/1=1
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