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Math Help - Simplify the expression

  1. #1
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    Question Simplify the expression

    (18x^3y^4)^{-1}(3x^4y)^4

    The answer I came up with was: 54x^{13}y
    but I feel this answer is incorrect. Please, what is the correct answer and how does one get it?

    Thanks in advance!
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  2. #2
    Moo
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    Hello,

    There are three main things to do :

    - (a^b)^c = a^{bc}
    - a^b a^c = a^{b+c}
    - (ab)^c = a^c b^c

    And note that 18 is 3*2
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  3. #3
    Senior Member topher0805's Avatar
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    <br />
(18x^3y^4)^{-1}(3x^4y)^4<br />

    Recall that (18x^3y^4)^{-1} = \frac {1}{(18x^3y^4)}

    So you would have:

    \frac {81x^{16}y^4}{18x^3y^4}

    Factor out a 9:

    \frac {9x^{16}y^4}{2x^3y^4}

    Factor out an x^3:

    \frac {9x^{13}y^4}{2y^4}

    Factor out a y^4:

    \frac {9x^{13}}{2}
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