1. Sep 9, 2008

### Embison

I'm reading Basic Math & Pre Algebra for Dummies and it says...

"As you can see, the notation 2 to the power of 4 means multiply 2 by itself 4 times."

and this is written there...2 to the power of 4 = 2 X 2 X 2 X 2 = 16

Isn't that multiplied 3 times? 2 X 2 = 4 that's once. then 4 X 2 = 8 that's twice. then 8 X 2 = 16 that's three times.

2. Sep 9, 2008

### symbolipoint

We have some trouble with language and wording. The exponent indicates the count of a number as a factor in a term.

"Two to the power of Four", "2 to the power of 4", means 2*2*2*2 = 16.
COUNT the factors of 2. How many factors of 2 are used? The expression uses 4 factors of 2. The exponent is 4.

3. Sep 14, 2008

### özgürden

2^4 means 2 multiplied with itself 4 times.

2 is called the base

4 is called the power

but..x^0 = 1 implies that x ≠ 0 ..why?
proof?

4. Sep 14, 2008

### HallsofIvy

Staff Emeritus

0x= 0 for any positive x. But x0= 1. That is, the limit as x approaches 0 of 0x is 0 while the limit, as x approaches 0 of x0 is 1. In order to have a continuous function we would want to define the value to be such a limit. Since those two limits both "represent" 00, but are different, 00 has no value.

5. Sep 14, 2008

### rbj

i would agree that this should be in another thread, but i'm not gonna start it.

Halls, because

$$\lim_{x \rightarrow 0} x^x = 1$$

i think most people agree that, if you were gonna assign a value of 00 to anything, it would be 1. heck, (0.000000001)0.000000001 is a lot closer to 1 than it is to 0.

6. Sep 14, 2008

### tiny-tim

Hi Embison!
Yup … I agree with you!

But it's ok in that book …

'cos dummies won't notice!

7. Sep 14, 2008

### disregardthat

But this is only if the exponent and base is approaching zero at the same rate. In fact, $$\lim_{x \to 0} \lim_{y \to 0} x^{y}$$ can take any value, depending on the "speed" the two variables are approaching zero with.

8. Sep 15, 2008

pardon..