The expression `(root(4)(32x^11*y^15))/(root(4)(2x^3y^2))` has to be simplified.

`(root(4)(32x^11*y^15))/(root(4)(2x^3y^2))`

= `(32x^11*y^15)^(1/4)/(2x^3y^2)^(1/4)`

= `((32x^11*y^15)/(2x^3y^2))^(1/4)`

= `(32/2)^(1/4)*x^((11-3)/4)*y^((15 - 2)/4)`

= `16^(1/4)*x^(8/4)*y^(13/4)`

= `2*x^2*y^(13/4)`

**The simplified form of **`(root(4)(32x^11*y^15))/(root(4)(2x^3y^2)) = 2*x^2*y^(13/4)`