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An example illustrating the laws of exponents

  1. Apr 26, 2007 #1
    Using the well-known rule for multiplying numbers raised to powers:

    [tex]u^{\frac{a}{b}}v^\frac{c}{d}} = (uv)^{\frac{a+c}{b+d}}[/tex],

    [tex]3^{2/3}9^{7/6} = (3*9)^{\frac{2+7}{3+6}} = 27[/tex]

    If you can think of a better way I'd sure like to see it! :biggrin:
    Last edited: Apr 26, 2007
  2. jcsd
  3. Apr 26, 2007 #2


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    Wow, that is so easy! I never though about it like that before. I always used to do it the hard way.
  4. Apr 26, 2007 #3
    Wont work if a or c is zero though. Probably why its not a rule.

    And, that rule only applies when they have the same base. You cant just add exponents like that with different basii.

    Uh yeah, your formula isint working for a lot of numbers.
    Last edited: Apr 26, 2007
  5. Apr 26, 2007 #4
    Yeah it looks like it is not as general as he stated it. Looks like an infinite number of examples that it does not work for.

    Consider flipping the fractions.

    [tex]3^{3/2}9^{6/7} = 34.1668 \neq (3*9)^{\frac{3+6}{2+7}} = 27[/tex]
    Last edited: Apr 26, 2007
  6. Apr 27, 2007 #5
    Not only are the bases different but a/c + b/d is not equal to (a+b)/(c+d). :confused: I think the OP is referring to a completely different "rule" than you are referring to.
  7. Apr 27, 2007 #6

    more text
  8. Apr 27, 2007 #7
    That's why it's so funny!!! :rolleyes: You get the right answer, but for the wrong reasons!
  9. Apr 27, 2007 #8
    :rolleyes: As mentioned above, that only works in like one case. I don't see the point of this thread.
  10. Apr 27, 2007 #9
    that's what's so funny though, it's totally wrong except the answer is correct anyway
  11. Apr 27, 2007 #10
    Ha ha? :confused:
  12. Apr 27, 2007 #11


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    Wow.. if you find that funny you need to get out more.

    Seriously though, there are infinitely many "formulae" one can construct that are incorrect but hold coincidentally give the correct answer in one or two cases. However, there is no merit to be had in discussing such "formulae".
  13. Apr 27, 2007 #12
    I guess I need to get out more.
  14. Apr 27, 2007 #13
    no, I think if you don't find it funny then YOU should get out more... & lighten up. :grumpy: But on the other hand, it isn't the funniest math joke I know, which is still [tex]\lim_{8\rightarrow 9}\sqrt{8} = 3[/tex]
    Last edited: Apr 27, 2007
  15. Apr 27, 2007 #14

    or are you joking?
  16. Apr 27, 2007 #15
    Now thats funny :rofl:
  17. Apr 27, 2007 #16
    I smirked.
  18. Apr 27, 2007 #17
    I take it my sarcasm/joke meter is defunct?
  19. Jan 8, 2009 #18
    33/2 +96/7=33/2 +312/7
    = only which is 11.771552
    Last edited by a moderator: Jan 8, 2009
  20. Jan 8, 2009 #19
    Why not just ...

    ua/bvc/d = ua/buk*c/d

  21. Jan 8, 2009 #20
    It reminds me of simplifying [tex]\frac{16}{64}[/tex] by canceling out the sixes.
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