Question 268985
{{{root(3,(729x^8)/(y^3))}}} Start with the given expression.



{{{root(3,729x^8)/root(3,y^3)}}} Break up the root.



{{{root(3,9^3x^8)/root(3,y^3)}}} Rewrite 729 as {{{9^3}}}



{{{root(3,9^3x^3*x^3*x^2)/root(3,y^3)}}} Factor {{{x^8}}} to get {{{x^3*x^3*x^2}}}



{{{(root(3,9^3)*root(3,x^3)*root(3,x^3)*root(3,x^2))/root(3,y^3)}}} Break up the root in the numerator.



{{{(9x*x*root(3,x^2))/y}}} Evaluate the cube roots of {{{9^3}}}, {{{x^3}}} and {{{y^3}}} to get 9, 'x', and 'y'.



{{{(9x^2*root(3,x^2))/y}}} Multiply



So {{{root(3,(729x^8)/(y^3))=(9x^2*root(3,x^2))/y}}} where {{{y<>0}}}