[tex]\displaystyle \\
\frac{1}{3} \sqrt{27} =\sqrt{ \left( \frac{1}{3} \right)^2\times 27} =\sqrt{ \frac{1}{9} \times 27} =\sqrt{ \frac{27}{9} } = \boxed{\sqrt{3} }\\ \\ \\ \\
-2\sqrt{ \frac{1}{8} }= \sqrt{(-2)^2 \times \frac{1}{8} }= \sqrt{4 \times \frac{1}{8} }= \sqrt{ \frac{4}{8} }= \boxed{\sqrt{ \frac{1}{2} }}[/tex]