\[\boxed{\mathbf{361}\mathbf{.}}\]
\[1)\ 2\frac{6}{7}\ :\left( \frac{5^{\backslash 7}}{6} - \frac{9^{\backslash 3}}{14} \right) =\]
\[= \frac{20}{7}\ :\frac{35 - 27}{42} = \frac{20}{7}\ :\frac{8}{42} =\]
\[= \frac{20}{7} \cdot \frac{42}{8} = \frac{5 \cdot 6}{1 \cdot 2} = 5 \cdot 3 = 15\]
\[2)\ 2\frac{6}{7}\ :\frac{5}{6} - \frac{9}{14} = \frac{20}{7} \cdot \frac{6}{5} - \frac{9}{14} =\]
\[= \frac{24^{\backslash 2}}{7} - \frac{9}{14} = \frac{48 - 9}{14} = \frac{39}{14} =\]
\[= 2\frac{11}{14}\]