Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    [tex]2^9=(2^3)^3[/tex]

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

    HallsofIvy

    User Avatar
    Science Advisor

    In that case, it's good to have a calculator that is smarter than you are!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook