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Dealing with exponent laws (2 simple questions in one thread)

  1. Feb 6, 2008 #1
    1. The problem statement, all variables and given/known data

    6^1+6^-1 / 6^1-6^-1 (Question is to evaluate that, but I am going to venture to guess that we are supposed to somehow simplify the question a lot further. We just finished learning all the exponent laws)

    Explain how you can tell which is bigger without evaluating: 20^100 or 400^20 ?

    Have not been able to evaluate at all.
  2. jcsd
  3. Feb 6, 2008 #2
    x^-1 = 1/x

    From there, you can finish it a number of ways. I'd probably just combine the fraction & then divide the whole thing to get a fraction result.

    To find which is larger, they both start with 6, & either add or subtract x^-1. If you add a positive number to 6 or subtract a negative number, the positive number will be larger.
  4. Feb 6, 2008 #3
    OH! haha. The second part with "which is bigger" is a whole differnt question. Sorry I didn't make that clear :P .

    Anyways, since only the fist question was answered with accuracy here, I would like to discus that quickly. How do you combine the fraction like you say? That is where I am getting mixed up: Rearranging to get all positive exponents.
  5. Feb 6, 2008 #4


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    [tex]\frac{6+ 6^{-1}}{6- 6^{-1}}[/tex]
    Multiply both numerator and denominator by 6.

    [itex]20= 2^2(5)[/itex] so [itex]20^{100}= 2^{200}(5^{100})[/itex]. [itex]400= 40(100)= (8*5)(4*25)= 2^5(5^3)[/itex] so [itex]400^{20}= 2^{100}(5^{60})[/itex]
    Can you compare those?

  6. Feb 6, 2008 #5
    ahhh! Yes, I see for both now. I understand the first one and well... The second one, I get the idea of making them both have similar bases but how you did it would take a little more concentration on my behalf. I will do that after posting this but I must thank you for your work.
  7. Feb 6, 2008 #6
    Actually, it is easier to solve if you see that [itex]400 = 20^2[/itex]. from which you get that [itex]400^{20} = 20^{2 * 20} = 20^{40}[/itex] and of course [itex]20^{100} > 20^{40}[/itex].

    EDIT: It's a property of exponents that [itex](a^b)^c = a^{bc}[/itex]
    Last edited: Feb 6, 2008
  8. Feb 6, 2008 #7
    You're right. I understand that now, no problem. Thanks for your help as well! :)
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