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Math Help - dividing polynomials

  1. #1
    Junior Member
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    37

    Smile simple problem

    What I need to do here?
    8^6*3^20+2^18*9^10
    6^19

    Hope you can help me
    Thanks
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  2. #2
    MHF Contributor
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    If this is a simple problem for everybody, then there are no difficult problems.
    It is simple for those who know how to solve it.
    I can solve it in 3 lines only, but can you follow the solution?

    [8^6 *3^20 +2^18 *9^10] / 6^19
    = [2^18 *3^20 +2^18 *3^20] / 2^19 *3^19
    = 2^19 *3^20 / 2^19 *3^19
    = 3 --------answer.

    Simple for me.

    (Maybe, next time, avoid calling any Math problem "simple" so that, I, at least, can explain the solution in details.)
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  3. #3
    Newbie
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    Wink here is a little more explanation

    Maybe Ticbol had a bad day.
    I would guess that dgolverk does not speak english as a first language and probably did not mean much by calling the post 'simple problem.'

    8^6*3^20+2^18*9^10
    6^19

    8^6 can be written as (2^3)^6 or 2^18; (x^a)^b = x^(a*b)

    2^18*3^20+2^18*9^10
    6^19

    9^10 can be written as (3^2)^10 or 3^20

    2^18*3^20+2^18*3^20
    6^19

    2^18 +2^18 can be written as 2^19; x^a + x^a = x^(a+1)

    2^19*3^20
    6^19

    6^19 can be written as 2^19*3^19; (a*b)^c = a^c * b^c

    then you can simplify

    2^19*3^20
    2^19*3^19

    to get 3
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  4. #4
    MHF Contributor
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    "2^18 +2^18 can be written as 2^19; x^a + x^a = x^(a+1)"

    No.
    x^a +x^a = 2(x^a), not x^(a+1).

    x^(a+1) is (x^a)*x ---------***

    2^18 +2^18 is equal to 2^19 because
    2^18 +2^18
    = 2(2^18)
    = 2^(1+18)
    = 2^19
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  5. #5
    Junior Member
    Joined
    Oct 2005
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    Thanks for helping guys!
    I wrote "simple problem" because I knew that you know how to slove that, and for you it's simple.
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