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# Why is....?

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65
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why is 0^0=1?

Guest Oct 19, 2017

#2
+26329
+2

Hmm!!

0^0 is undefined.

Alan  Oct 19, 2017
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#1
+432
0

Anything to the power of 0 is 1.

[Edited]

And here's why.

Let's first assume 3^0 is 1.

So...

3^0 =1.

3^1=3.

3^2=9.

3^3=27.

3^4=81.

Now as you can see, a number is 3 times greater than the number before it. Here's what I'm talking about.

3^2 is 9 and 3^3 is 27. It is obvious that 27 is 3 times greater than 9. This is the same with other numbers that is in the

"3-to-the-what power" form.

So if you think about it, shouldn't 3^0 be 1?

Because we know that a number is 3 times greater than the number before it.

And 3^1 is 3. So we have to divide that by 3 to get "3^0."

3/3 is 1.

So 3^0 is 1.

This concept can be hard to understand with one example.

But think about it. A similar rule applies to any other set of exponents with the same base.

2^1 (That 's 2) divided by 2 would get us 2^0.  And 2^0=1. See a pattern?

So you see that you can divide a number with an exponent by its base to get the number that has an exponent 1 less than the original number's exponent. (example: 2^2 and 2^1.  2^1 has an exponent 1 less than 2^2. )

And that's my explanation.

There are probably many simpler and better-to-understand explanations out there...

Correct me if my explanation is wrong. I often get things mixed up in explaining things.

Gh0sty15  Oct 19, 2017
edited by Gh0sty15  Oct 19, 2017
#2
+26329
+2

Hmm!!

0^0 is undefined.

Alan  Oct 19, 2017
#3
+432
0

Wow...I went through all that for nothing?

Gh0sty15  Oct 19, 2017
#4
+432
0

This calculator says 0.

Which one is right?

Gh0sty15  Oct 19, 2017
#5
+1

WolframAlpha is a better "Authority" on these matters. Try it and says 0^0 ="undefined".

Guest Oct 19, 2017
#6
+432
+1

Thanks, Guest.

Sorry Alan. (I think I've said that the last time I've made a mistake on an explanation)

Gh0sty15  Oct 19, 2017
#7
+91027
0

So long as you learned from your mistake that is all that is important :)

Melody  Oct 19, 2017

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