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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:

(3^{n}-3^{n-1})

Which after factoring becomes

3^{n-1}(3-1)

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 3^{n}/3^{n-1}which equals 3, but this somehow confused me more.

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# Can someone explain why the exponents behave like this

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