Question 264531
{{{root(3,(512x^5)/(y^3))}}} Start with the given expression.



{{{root(3,512x^5)/root(3,y^3)}}} Break up the root.



{{{root(3,8^3x^5)/root(3,y^3)}}} Rewrite 512 as {{{8^3}}} (since {{{512=8^3}}})



{{{root(3,8^3x^3x^2)/root(3,y^3)}}} Rewrite {{{x^5}}} as {{{x^3x^2}}} (since {{{x^5=x^3x^2}}})



{{{root(3,8^3)root(3,x^3)root(3,x^2)/root(3,y^3)}}} Break up the root in the numerator.



{{{(8*root(3,x^3)root(3,x^2))/root(3,y^3)}}} Evaluate the cube root {{{8^3}}} to get 8. Remember the cube root of anything cubed is simply that original expression. In other words, {{{root(3,x^3)=x}}}. This is why everything was broken down into parts dealing with cubes.



{{{(8x*root(3,x^2))/root(3,y^3)}}} Evaluate the cube root {{{x^3}}} to get 'x'.



{{{(8x*root(3,x^2))/y}}} Evaluate the cube root {{{y^3}}} to get 'y'.



So {{{root(3,(512x^5)/(y^3))=(8x*root(3,x^2))/y}}} where {{{y<>0}}}