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Math Help - rational expontent problem

  1. #1
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    rational expontent problem

    the problem is as follows:

    write the expression in simplest form

    2/(81^(1/6))



    can you explain step by step how to do this?

    the answer is supposed to be:

    2(3^(1/3)) / 3

    i posted this somwhere else too but i wasnt getting a reply quickly enough sorry
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  2. #2
    MHF Contributor
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    Quote Originally Posted by talhaguy View Post
    the problem is as follows:

    write the expression in simplest form

    2/(81^(1/6))



    can you explain step by step how to do this?

    the answer is supposed to be:

    2(3^(1/3)) / 3

    i posted this somwhere else too but i wasnt getting a reply quickly enough sorry
    2 / [81^(1/6)]
    = 2 / [(3^4)^(1/6)]
    = 2 / [3^(4/6)]
    = 2 / [3^(2/3)]
    Now rationalize the denominator,
    Multiply both numerator and denominatoe by 3^(1/3),
    = [2 *3^(1/3)] / [3^(2/3) *3^(1/3)]
    = [2 *3^(1/3)] / [3^(2/3 +1/3)]
    = [2 *3^(1/3)] / [3^(3/3)]
    = [2 *3^(1/3)] / [3^(1)]
    = [2 *3^(1/3)] / 3 ------------answer
    or,
    = (2/3)*3^(1/3) ---------answer
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  3. #3
    Grand Panjandrum
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    Don't make double posts it wastes moderators and helpers time, and
    confuses everybody.

    RonL
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  4. #4
    Super Member

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    Hello, talhaguy!

    Write the expression in simplest form: . \frac{2}{81^{\frac{1}{6}}}

    The answer is: . \frac{2\cdot3^{\frac{1}{3}}}{3}

    This is identical to ticbol's solution . . . written in LaTeX.

    . . \frac{2}{81^{16}} \;=\;\frac{2}{\left(3^4\right)^{\frac{1}{6}}} \;=\;\frac{2}{3^{\frac{4}{6}}} \;=\;\frac{2}{3^{\frac{2}{3}}}

    Rationalize: . \frac{2}{3^{\frac{2}{3}}}\cdot\frac{3^{\frac{1}{3}  }} {3^{\frac{1}{3}}} \;=\;\boxed{\frac{2\cdot3^{\frac{1}{3}}}{3}}

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