Answer:
Option D :- [tex] \sf \: 18 {x}^{2} {y}^{2} \sqrt[3]{3 {xy}^{2} }[/tex]
Step-by-step explanation:
[tex] \sf \: 3x\sqrt[3]{648 {x}^{4} {y}^{8} }[/tex]
transform the equation
[tex] \rightarrow \sf \: 3x\sqrt[3]{ {6}^{3} \times {3x}^{2} \times {xy}^{6} \times {y}^{2} }[/tex]
rewrite the expression
[tex] \rightarrow \sf \: 3x \times \sqrt[3]{ {6}^{3}} \times\sqrt[3]{ {3x}^{2}} \times \sqrt[3]{ {xy}^{6} } \times \sqrt[3]{{y}^{2} }[/tex]
Simplify the radical expression
[tex] \rightarrow \sf \: 3x \times {6xy}^{2} \sqrt[3]{3xy {}^{2} }[/tex]
Multiply
[tex] \sf \: 18 {x}^{2} {y}^{2} \sqrt[3]{3 {xy}^{2} }[/tex]
