Question 1125364
Looking for help with the following radical, which needs to be simplified. The book does NO help in explaining how to go about it. 
^3sqrt -27y^18/81x^6

After scouring the internet I used quotient rules and broke it down as follows:

^3sqrt-27y^18 / ^3sqrt81x^6

This gave me a result of:

3y^6/3sqrt3^4x^2

Am I on the right track? Thank you!
<pre>This is what you came up with: {{{3y^6/3sqrt(3^4x^2)}}}, I believe.
If this is so, then I must say that you're NOT on the right track. Hopefully, the simplification below will steer you onto the right path.
{{{root(3, (- 27y^18)/(81x^6))}}} ========> {{{root(3, ((- 3)^3(y^6)^3)/3(3)^3(x^2)^3))}}} ======> {{{root(3, (- 1(3)^3(y^6)^3)/3(3)^3(x^2)^3))}}} =======> {{{root(3, (- 1cross((3)^3)(y^6)^3)/3cross((3)^3)(x^2)^3))}}} =======> {{{highlight(highlight_green(highlight((y^6/x^2)root(3, - 1/3))))}}}
OR, RATIONALIZING the DENOMINATOR in the RADICAND, we get:
{{{(y^6/x^2)root(3, - 1/3)}}} ===> {{{(y^6/x^2)(root(3, - 1)/root(3, 3))}}} ===> {{{(y^6/x^2)((- 1)/root(3, 3))}}} ===> {{{(y^6/x^2) * ((- 1(root(3, 3))^2)/root(3, 3)(root(3, 3))^2))}}} =======> {{{(y^6/x^2) * ((- 1(root(3, 3))^2)/(root(3, 3))^3))}}} ===> {{{(y^6/x^2) * ((- 1(root(3, 3))^2)/3)}}} ===> {{{highlight(highlight_green(highlight((- 1/3)(y^6/x^2) * (root(3, 3))^2))))}}}, or {{{highlight(highlight_green(highlight((- y^6/(3x^2)) * (root(3, 3))^2))))}}}