Question 878426
The key is to break up whatever you can into cube roots



{{{root(3,8x^2y^3z^4)}}}



{{{root(3,8)*root(3,x^2)*root(3,y^3)*root(3,z^4)}}}



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



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



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



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



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



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



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



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



{{{2yz*root(3,x^2z)}}}



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So, {{{root(3,8x^2y^3z^4)}}} simplifies to {{{2yz*root(3,x^2z)}}}