Answer: First option.
Step-by-step explanation:
If the radicals have the same index and the same radicands, they can be added.
Descompose 16 and 54 into their prime factors:
[tex]16=2*2*2*2=2^3*2\\54=2*3*3*3=2*3^3[/tex]
Remember that:
[tex]\sqrt[n]{x^n}=x[/tex]
Then, rewriting and simpliying, you get:
[tex]=2(\sqrt[3]{16x^3y})+4(\sqrt[3]{54x^6y^5})\\\\=2(\sqrt[3]{2^3*2x^3y})+4(\sqrt[3]{2*3^3*x^6*y^3*y^2})\\\\=2(2x\sqrt[3]{2y})+4(3x^2y(\sqrt[3]{2y^2}))\\\\=4x(\sqrt[3]{2y})+12x^2y(\sqrt[3]{2y^2})[/tex]
