$$2 \frac { 16 } { 17 } \cdot 3 \frac { 2 } { 5 } : \frac { 11 } { 12 } \cdot 2 \frac { 1 } { 5 } : 2 \frac { 2 } { 3 }$$
$9$
$$\frac{\frac{\frac{34+16}{17}\times \frac{3\times 5+2}{5}}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{\frac{50}{17}\times \frac{3\times 5+2}{5}}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{\frac{50}{17}\times \frac{15+2}{5}}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{\frac{50}{17}\times \frac{17}{5}}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{\frac{50\times 17}{17\times 5}}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{\frac{50}{5}}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{10}{\frac{11}{12}}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{10\times \frac{12}{11}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{10\times 12}{11}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{120}{11}\times \frac{2\times 5+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{120}{11}\times \frac{10+1}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{120}{11}\times \frac{11}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{120\times 11}{11\times 5}}{\frac{2\times 3+2}{3}}$$
$$\frac{\frac{120}{5}}{\frac{2\times 3+2}{3}}$$
$$\frac{24}{\frac{2\times 3+2}{3}}$$
$$\frac{24}{\frac{6+2}{3}}$$
$$\frac{24}{\frac{8}{3}}$$
$$24\times \frac{3}{8}$$
$$\frac{24\times 3}{8}$$
$$\frac{72}{8}$$
$$9$$
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$3^{2}$