Powers and simplifications, please help me

This is a discussion on Powers and simplifications, please help me within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Can anyone explain for me how: -24x^6y^7 --------------- 18x^-3y^9 becomes -4x^9 -------- 3y^2 ? Sorry if I am using this ...

  1. #1
    Registered User
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    Powers and simplifications, please help me

    Can anyone explain for me how:

    -24x^6y^7
    ---------------
    18x^-3y^9

    becomes

    -4x^9
    --------
    3y^2 ?

    Sorry if I am using this board as a place to ask about maths.......If you have any good link to some good maths questions forum, then I'd be very glad to have it.

  2. #2
    Toaster Zach L.'s Avatar
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    2,686
    Just play around with the following two properties a bit, and you'll get it:

    (x^a)*(x^b)=x^(a+b)
    x^(-a)=1/(x^a)
    The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.

  3. #3
    Registered User
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    Jan 2003
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    648
    Expanding the exponents you get:

    -24 * x * x * x * x * x * x * y * y * y * y * y * y * y
    ----------------------------------------------------------------------
    18 * 1/x * 1/x * 1/x * y * y * y * y * y * y * y * y * y

    I bet you know that y/y = 1, so we can cross out 7 y on the top and bottom. Next, when you have a fraction on the bottom part, you can flip the bottom part of that fraction to the top of the main one. So:

    a
    ---
    b/c

    ...becomes ac / b.

    Doing that, those 3 reciprocals of x in the bottom get on top, making 7 x on top.

    Next you simplify the numbers which is real simple here. Both have a common factor of 6, so you factor that out (-24 / 6 = -4, 18 / 6 = 3).

    And you end up with:

    -4 * x^9
    ------------
    3 * y^2

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