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Can someone explain why the exponents behave like this

  1. Jul 11, 2012 #1

    I can't seem to wrap my mind around this. I understand exponent properties, but for some reason when you throw that n in there it rocks my world.

    I was solving an induction problem, and a piece of the algebra that I sort of guessed at was this:

    Which after factoring becomes

    I do not understand how the exponential division is working here with the n. Can someone please explain?

    I tried testing it out a different way by just writing 3n/3n-1 which equals 3, but this somehow confused me more.
    Last edited: Jul 11, 2012
  2. jcsd
  3. Jul 11, 2012 #2

    If you understand [itex]\,xy-x=x(y-1)\,[/itex], which is a simple application of the distributivity axiom (in some

    field), then putting [itex]\,x=3^{n-1}\,\,,\,y=3\,[/itex] , we get:
    [tex]3^n-3^{n-1}=3^{n-1}\cdot 3 -3^{n-1}=3^{n-1} (3-1)=2\cdot 3^{n-1}[/tex]

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