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Something I should really know by now

  1. Nov 1, 2005 #1
    Idk if this is right
    [tex] e^{n^2} = (e^n)^n [/tex]
    Atleast I didn't think [tex] e^{n^2} = e^n*e^n [/tex]

    I had a test in calc 3 today, and that was part of a series. If it is equal (in the first equation) then I did it right, otherwise not. I came up with convergent, and someone else said they used an integral and got convergent, so...my answer hinges on that, which i should really know by now :)
    Last edited: Nov 1, 2005
  2. jcsd
  3. Nov 1, 2005 #2
    In general, [tex]a^{b^c} \ne a^{bc}[/tex].
    [tex](a^b)^c = a^{bc}[/tex]
    You should be able to show this yourself. Your first equality is correct.
  4. Nov 1, 2005 #3
    Well, when in doubt just substitute some numbers! I don't understand why people don't do this more often when in doubt.

    Like pretend e=2 and that n=3


    we all know [tex]2^9=512[/tex] and [tex]2^3=8[/tex]
    so it works

    Now, this is aside from the fact that this is a basic algebraic rule...
  5. Nov 1, 2005 #4
    yea, lol, i just typed in [tex]({e^n})^n[/tex] into my calculator and it spit back [tex]e^{n^2}[/tex]... it's a ti-89.

    sometimes you just forget the basic stuff...
  6. Nov 1, 2005 #5


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    Science Advisor

    In that case, it's good to have a calculator that is smarter than you are!
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