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Multiply the radicals: (x^3 y)^1/4 * (x^2 y^2)^1/3Please show solution with everything...

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spock9 | Student, Undergraduate | (Level 1) Honors

Posted May 3, 2012 at 5:22 PM via web

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Multiply the radicals: (x^3 y)^1/4 * (x^2 y^2)^1/3

Please show solution with everything in its simplest form.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 3, 2012 at 5:32 PM (Answer #1)

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The product `(x^3y)^(1/4)*(x^2 y^2)^(1/3)` has to be determined

`(x^3 y)^(1/4) * (x^2 y^2)^(1/3)`

=>`x^(3/4)*x^(2/3)*y^(1/4)*y^(2/3)`

=> `x^(3/4 + 2/3)*y^(1/4 +2/3)`

=> `x^(17/12)*y^(11/12)`

The product of `(x^3y)^(1/4) * (x^2 y^2)^(1/3) = x^(17/12)*y^(11/12)`

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