1) \(\left[\left(\frac{15}{23}-\frac{11}{33}\right)\cdot\frac{21}{29}+6\frac{6}{7}:\frac{16}{21}\right]:16\frac{1}{2}\)

\(\frac{15}{23}-\frac{11}{33}=\frac{22}{69}\).

\(\frac{22}{69}\cdot\frac{21}{29}=\frac{22}{95}\).

\(6\frac{6}{7}:\frac{16}{21}=\frac{48}{7}\cdot\frac{21}{16}=9\).

Тогда выражение равно:

\(\left(\frac{22}{95}+9\right):16\frac{1}{2}=\frac{877}{95}:\frac{33}{2}=\frac{877}{95}\cdot\frac{2}{33}=\frac{1754}{3135}\).

Ответ: \(\frac{1754}{3135}\).