How to simplify $root(3)(24y^21x^5)$ ?

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Answer 1 · 2017-04-02T18:39:43

$2xy^7root(3)(2x^2)$

Write the radicand as aproduct of prime factors.

$root(3) (24y^21x^5) =root(3) (3xx2^3y^21x^5)$

Write cubes where possible:
$root(3) (3xx2^3y^21x^5) = root(3) (3xxcolor(red)(2^3y^21x^3)xx x^2)$

Find the cube roots where possible by dividing the indices by $3$ .

$=color(red)(2xy^7)root(3)(2x^2)$

How to simplify root(3)(24y^21x^5)root(3)(24y^21x^5) ?