Question 1125364
What you are given is not clear.  Maybe you are asking for the cube root of something,...


{{{root(3,((-27y^18)/(81x^6)))}}}


{{{root(3,((-1*3^3*(y^6*y^6*y^6))/(3*3^3*(x^2)^3)))}}}


You may simplify what is inside first:
{{{root(3,((-1*cross(3^3)*(y^3*y^6*y^6*y^6))/(3*cross(3^3)*(x^2)^3)))}}}


{{{root(3,((-1*y^6*y^6*y^6)/(3*(x^2)^3)))}}}


You need to understand  {{{root(3,C^3)=C}}} and also  {{{(root(3,C))^3=C}}}.


Continuing....

{{{((y^6)/(x^2))root(3,-1/3)}}}
and you can rationalize the denominator if you want to or need to.


{{{-(y^6/x^2)root(3,1/3)}}}


{{{-(y^6/x^2)root(3,1/3)root(3,3/3)root(3,3/3)}}}


{{{-(1/3)(y^6/x^2)(root(3,3))^2}}}