Вычислите: \(2\frac{1}{5} : \left(\frac{16}{25}+\frac{7}{20}\right)-\frac{16}{7}\cdot1\frac{8}{27}\).

\[2\frac{1}{5}=\frac{11}{5},\qquad \frac{16}{25}+\frac{7}{20}=\frac{64}{100}+\frac{35}{100}=\frac{99}{100}.\]

\[\frac{11}{5}:\frac{99}{100}=\frac{11}{5}\cdot\frac{100}{99}=\frac{20}{9}.\]

\[1\frac{8}{27}=\frac{35}{27},\qquad \frac{16}{7}\cdot\frac{35}{27}=\frac{80}{27}.\]

\[\frac{20}{9}-\frac{80}{27}=\frac{60}{27}-\frac{80}{27}=-\frac{20}{27}.\]

Ответ: \(-\frac{20}{27}\).