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Math Help - dividing polynomials

  1. #1
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    dividing polynomials

    4x^-1y
    10xy^-2

    Now I know its 2/5 but I just dont know what to do with the negative exponents.

    Another quick one.... (3/4)^-2
    Is that just 9/8?

    And I don't believe this is factorable... 36x^2 +49
    Am I right?
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by toddsayshi View Post
    4x^-1y
    10xy^-2

    Now I know its 2/5 but I just dont know what to do with the negative exponents.
    Do you know negative exponents? x^{-y}=\frac{1}{x^y} and  \frac{1}{x^{-y}}=x^y

    So you have: \frac{4yx{-1}}{10xy^{-2}}

    I would split it up to be: \frac{4y}{10x}\times x^{-1}\times \frac{1}{y^{-2}}

    Now get rid of the negative exponents: \frac{4y}{10x}\times \frac{1}{x}\times y^2

    Multiply to get: \frac{4y \times y^2}{10x\times x}

    Therefore: \frac{4y^3}{10x^2}

    Which can be changed to: \frac{2y^3}{5x^2}

    but that's as far as you can go.


    Another quick one.... (3/4)^-2
    Is that just 9/8?
    \left(\frac{3}{4}\right)^{-2}=\frac{3^{-2}}{4^{-2}}=\frac{4^2}{3^2}=\frac{16}{9}

    And I don't believe this is factorable... 36x^2 +49
    Am I right?
    I don't think it is, but 36x^2-49 is.
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  3. #3
    Junior Member Dergyll's Avatar
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    Here is a link that clears the negative exponents, it basically means something like this:

    N^-x = 1/N^x

    Math Forum - Ask Dr. Math Archives: Negative Exponents

    On top of your problem there, is it 4x^-1 and then multiply by "y" or is it just 4x to the negative 1y power?

    And the factoring, you can't factor that, but if in between it was a minus sign then you can: 36x^2-49 = (6x+7)(6x-7)

    Hope this helps
    Derg
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  4. #4
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    Quote Originally Posted by Dergyll View Post
    Here is a link that clears the negative exponents, it basically means something like this:

    N^-x = 1/N^x

    Math Forum - Ask Dr. Math Archives: Negative Exponents

    On top of your problem there, is it 4x^-1 and then multiply by "y" or is it just 4x to the negative 1y power?

    And the factoring, you can't factor that, but if in between it was a minus sign then you can: 36x^2-49 = (6x+7)(6x-7)

    Hope this helps
    Derg

    It is 4x^-1 and then multiply by y.
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  5. #5
    Junior Member Dergyll's Avatar
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    Thats strange...I got the same answer with 2y^3/5x^2...are you sure it's 2/5 or are there other details?

    Derg
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  6. #6
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    Here it is....
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by toddsayshi View Post


    Here it is....
    Definitely \frac{2y^3}{5x^2} not 2/5.

    -Dan
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