We know that anything raised to the first power equals itself.

For example, (x)^1 = x. We also know that anything raised to the zero power equals 1. For example, (x)^0 = 1. Why is that true for both cases?

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- Dec 1st 2010, 05:36 PMRTC1996Exponent Rules: (x)^1 and (x)^0
We know that anything raised to the first power equals itself.

For example, (x)^1 = x. We also know that anything raised to the zero power equals 1. For example, (x)^0 = 1. Why is that true for both cases?

- Dec 1st 2010, 05:45 PMGrep
Well, makes sense, does it not? If it also follows that . One x multiplied together (so to speak) is just x.

Similar logic applies to . Zero x's multiplied together is obviously 0. [EDIT: Wow, I've handled x^0 enough times you'd think I wouldn't mess this up! x^0 = 1 as explained below. Let that be a lesson to me!]

Do note that 0^0 is a little tougher to settle. Why? An explanation can be found here:

sci.math FAQ: What is 0^0? - Dec 1st 2010, 05:45 PMdwsmith
- Dec 1st 2010, 05:46 PMdwsmith
- Dec 1st 2010, 05:47 PMelemental
...we know this.

We have shown one statement.

This is the other statement. - Dec 1st 2010, 05:49 PMGrep
- Dec 2nd 2010, 02:36 AMArchie Meade

We can get this result by forming the new index from 5-3.

Basically 3 of the x's in the denominator "cancel" 3 of the x's in the numerator to give 1.

Hence we can write the "general" way as shown in earlier posts.

Therefore, in index form... if we subtract the indices.

is 1 because it is an "index" way to write a number divided by itself.

Following on from this, you will see why negative indices represent a power of a number divided by a higher power of the same number.