\[\left( 15\frac{5^{\backslash 9}}{6} - 9\frac{25^{\backslash 2}}{27} \right) - 2\frac{17^{\backslash 3}}{18} =\]
\[= 15\frac{45}{54} - 9\frac{50}{54} - 2\frac{51}{54} =\]
\[= 13\frac{153}{54} - 11\frac{101}{54} =\]
\[= 2\frac{52}{54} = 2\frac{26}{27}\]