Is Exponents Multiplication or Repeated Multiplication?

[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.

 

[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.

 

[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?

 

[HallsofIvy]

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?

PLEASE do not add your own question to someone else's thread! Start your own thread.

0^x= 0 for any positive x. But x⁰= 1. That is, the limit as x approaches 0 of 0^x 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.

 

[rbj]

PLEASE do not add your own question to someone else's thread! Start your own thread.

0^x= 0 for any positive x. But x⁰= 1. That is, the limit as x approaches 0 of 0^x 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.

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

Halls, because

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

i think most people agree that, if you were going to 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.

 

[tiny-tim]

Hi 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.

Yup … I agree with you!

But it's ok in that book …

'cos dummies won't notice! ​

 

[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.

 

[özgürden]

PLEASE do not add your own question to someone else's thread! Start your own thread.

.

pardon..