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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

    symbolipoint

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    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?
    proof?
     
  5. Sep 14, 2008 #4

    HallsofIvy

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    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

    rbj

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    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

    tiny-tim

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    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

    disregardthat

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    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
    pardon..
     
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