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Math Help - Simplify: Write Answer Only Using Positive Exponents

  1. #1
    SSK
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    Simplify: Write Answer Only Using Positive Exponents

    (2x^-2 y^3/6xz^5)^-4

    Answer is 81x^12 z^20/y^12

    how is this so?
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  2. #2
    MHF Contributor
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    Hello SSK
    Quote Originally Posted by SSK View Post
    (2x^-2 y^3/6xz^5)^-4

    Answer is 81x^12 z^20/y^12

    how is this so?
    First, invert the fraction to get rid of the negative power outside the bracket:
     \left(\frac{2x^{-2} y^3}{6xz^5}\right)^{-4}=\left(\frac{6xz^5}{2x^{-2} y^3}\right)^{4}
    Then move the x^{-2} term to the numerator to get rid of its negative power:
    =\left(\frac{6xz^5x^2}{2 y^3}\right)^{4}
    (By the way, what I should more correctly say is: multiply top-and-bottom by x^2, and then note that in the denominator x^{-2}\times x^2 = 1. But it's quicker to say: move the x^{-2} term ...)

    Simplify:
    =\left(\frac{3x^3z^5}{y^3}\right)^{4}
    Lastly, remove the brackets by raising everything to the power 4:
    =\frac{81x^{12}z^{20}}{y^{12}}
    Grandad
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