1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about Exponents

  1. Sep 9, 2008 #1
    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. jcsd
  3. Sep 9, 2008 #2


    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    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.
  4. Sep 14, 2008 #3
    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?
  5. Sep 14, 2008 #4


    User Avatar
    Science Advisor

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

    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.
  6. Sep 14, 2008 #5


    User Avatar

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

    Halls, because

    [tex] \lim_{x \rightarrow 0} x^x = 1 [/tex]

    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.
  7. Sep 14, 2008 #6


    User Avatar
    Science Advisor
    Homework Helper

    Hi Embison! :smile:
    Yup … I agree with you! :biggrin:

    But it's ok in that book …

    :smile: 'cos dummies won't notice! :smile:
  8. Sep 14, 2008 #7


    User Avatar
    Science Advisor

    But this is only if the exponent and base is approaching zero at the same rate. In fact, [tex]\lim_{x \to 0} \lim_{y \to 0} x^{y}[/tex] can take any value, depending on the "speed" the two variables are approaching zero with.
  9. Sep 15, 2008 #8
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook