Zero as an Exponent
Date: 7/15/96 at 16:40:9 From: Anonymous Subject: Exponent of 0 Why do you get 1 when you take a number to the 0 power? Thanks! Thai-Meister
Date: 7/15/96 at 17:8:27 From: Doctor Paul Subject: Re: Exponent of 0 Let's first look at an example. Let's look at the list of numbers 3^1, 3^2, 3^3, 3^4, .... Finding the actual values, we get 3, 9, 27, 81, .... So what is the pattern in the bottom sequence? Well, every time you move to the right in the list you multiply by 3, and every time you move to the left in the list you divide by 3. So we could take the bottom sequence and keep going to the left and dividing by 3, and we'd have the sequence that looks like this: ..., 3^-3, 3^-2, 3^-1, 3^0, 3^1, 3^2, 3^3, 3^4, .... ..., 1/27, 1/9, 1/3, 1, 3, 9, 27, 81, .... So now we know what all the powers of 3 are! Actually, we just did the integer powers of 3. But that's probably enough for now. Now the trick is to show that you can do the same thing for any number, not just 3. It's actually not all that hard. So once you do that, you'll see that the x^0 term is always going to be 1, so that means that x^0 is 1 for all x (except maybe 0^0, but that's a whole other discussion)! -Doctor Paul, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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