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Simplify each expression

(-216)^1/3

My answer is 1/6. Am I correct.

(x^4y)^1/3 (xy^4)^2/3

I do not know how to simplify this.

  • Math -

    (-216)^1/3 = - 1/6

    (how can (1/6)(1/6)(1/6) end up negative ?

    (x^4y)^1/3 (xy^4)^2/3
    = (x^(13))(y^(1/3))(x^(2/3))(y^(8/3)
    = x^2 y^3

  • Math -

    1/6 is almost correct, except that you probably notice the original expression is negative. Give it one more try.

    Use the rules of exponentiation:
    (ab)^(m/n)=(a^m * b^m)^(1/n)
    and the inverse:
    (a^m)(1/n)
    =(a^(m/n))

    So
    (x^4y)^2/3 (xy^4)^1/3
    =( (x^4y)^2 * (xy^4) )^(1/3)
    =( x^8*y^2 * x * y*4 )^(1/3)
    =(x^9 * y^6)^(1/3)
    =x^3 * y^2

    (Note that the above example is not the same as the given question).

    Post your answer for a check if you wish.

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