False
Explanations:For the Left Hand side of the expression:
[tex]\sqrt[]{3}^{(3\sqrt[]{2})}[/tex]This can be simplified as:
[tex]\begin{gathered} 3^{\frac{1}{2}(3\sqrt[]{2})} \\ =3^{1.5\sqrt[]{2}} \\ =3^{2.12} \\ =\text{ }10.27 \end{gathered}[/tex]For the Right Hand Side of the expression:
[tex]\begin{gathered} (108)^{\frac{1}{6}} \\ =(108)^{0.167} \\ =\text{ }2.19 \end{gathered}[/tex]Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true
