math gre study ques

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a student starts with a positive number, x^6, and take the square root three times and the cube root once. this is equivalent to which of the following?

a. x^1/4

b. x^4/3

c. x^3/4

d. x^4

  • math gre study ques -

    (x^6)^(1/24) = x^(1/4)

  • math gre study ques -

    {(x^6)^[(1/2)^3]}^(1/3)

    [x^(6/8)]^(1/3)

    x^(2/8)

    x^1/4

    check with x = 2
    2^6 = 64
    sqrt = 8
    sqrt = 2sqrt 2
    sqrt = sqrt 2 sqrt (sqrt 2)
    = sqrt ( (sqrt2)^3)
    now take the cube root of that
    [sqrt (2 ^3/2)]^1/3
    sqrt (2^1/2) = 2^1/4 sure enough

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