\[\boxed{\mathbf{384}\mathbf{.}}\]
\[1)\ 1\frac{5^{\backslash 4}}{7} + 3\frac{11^{\backslash 2}}{14} - 2\frac{1^{\backslash 7}}{4} =\]
\[= 2 + \frac{20 + 22 - 7}{28} = 3 + \frac{35}{28} =\]
\[= 3 + 1\frac{7}{28} = 3 + 1\frac{1}{4} = 4\frac{1}{4}\]
\[2)\ 17\frac{2}{3} - \left( 6\frac{1^{\backslash 2}}{36} - 4\frac{3^{\backslash 9}}{8} \right) =\]
\[= 17\frac{2}{3} - \left( 6\frac{2}{72} - 4\frac{27}{72} \right) =\]
\[= 17\frac{2}{3} - \left( 5\frac{74}{72} - 4\frac{27}{72} \right) =\]
\[= 17\frac{2^{\backslash 24}}{3} - 1\frac{47}{72} =\]
\[= 17\frac{48}{72} - 1\frac{47}{72} = 16\frac{1}{72}\]