Question 487007
<pre>
{{{root(3,2x)*root(3,4x^2y^2)*root(3,2y^4)}}}

Write all as one cube root:

{{{root(3,(2x)(4x^2y^2)(2y^4))}}}

Break everything into prime factors:

{{{root(3,(2x)*(2*2xxyy)(2yyyy))}}}

Remove the parentheses:

{{{root(3,2x2*2xxyy2yyyy))}}}

Rearrange, putting like factors together:

{{{root(3,2*2*2*2xxxyyyyyy)}}}

Since the index of a cube root is 3, group
like factors by 3's:

{{{root(3,(2*2*2)*2(xxx)(yyy)(yyy))}}}

Write each group of 3 as a cube:

{{{root(3,(2^3)*2(x^3)(y^3)(y^3))}}}

Write as a product of cube roots:

{{{root(3,(2^3))root(3,2)root(3,x^3)root(3,y^3)root(3,y^3)}}}

To take the cube root of a cube, eliminate the radical and the exponent:

{{{2*(root(3,2))*xyy}}}

{{{2xy^2*root(3,2)}}}

Edwin</pre>