Çözüldü Radical and Exponential Variables (To be mentally solved in a few seconds)

https://i.ibb.co/35LTXKH3/exponential-and-radical.png
https://maktabkhooneh.org/mag/wp-content/uploads/2020/12/GRE-Prep-by-Magoosh.pdf
(Page 16, the multiple-choice example with no answer or explanation)

A is wrong because there is no such conversion.
B is wrong because (x^4·y^16)^(1 / 2) = [ (x^4)^(1 / 2) ]·[ (y^16)^(1 / 2) ] = x^2·y^8
C is wrong because (x·√y)(y·√x) = x·y·√(x·y)
D is correct because y·√x + y·√x = 2y·√x = (4y^2·x)^(1 / 2) = √(4y^2·x)
E is wrong because (x^y)·(y^y) = (x·y)^y.