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March 29, 2017

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Simplify - 2/(the 6th root of 81)

  • Algebra II - ,

    Let's break this down:

    The sixth root of 81 = 81^(1/6)
    81 is 9^2, so we have 9^(2*1/6) = 9^(1/3) or the cubed root of 9.

    Therefore, to get rid of the radical in the denominator, multiply by the equivalent of 1. Multiply by the cubed root of 3 divided by the cubed root of 3.

    2/(cubed root of 9) * (cubed root of 3)/(cubed root of 3)

    Now we have:
    2(cubed root of 3)
    ------------------
    (cubed root of 9)(cubed root of 3)

    2(cubed root of 3)
    ------------------
    (cubed root of 27)

    Finally:
    2(cubed root of 3)
    ------------------
    3

    I hope this helps.

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