$$9-1\frac{2}{9}\times3\frac{3}{11}\div5\frac{1}{7}\times\frac{7}{9}=$$
$\frac{680}{81}\approx 8.395061728$
$$9-\frac{\frac{9+2}{9}\times \frac{3\times 11+3}{11}}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{\frac{11}{9}\times \frac{3\times 11+3}{11}}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{\frac{11}{9}\times \frac{33+3}{11}}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{\frac{11}{9}\times \frac{36}{11}}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{\frac{11\times 36}{9\times 11}}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{\frac{36}{9}}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{4}{\frac{5\times 7+1}{7}}\times \frac{7}{9}$$
$$9-\frac{4}{\frac{35+1}{7}}\times \frac{7}{9}$$
$$9-\frac{4}{\frac{36}{7}}\times \frac{7}{9}$$
$$9-4\times \frac{7}{36}\times \frac{7}{9}$$
$$9-\frac{4\times 7}{36}\times \frac{7}{9}$$
$$9-\frac{28}{36}\times \frac{7}{9}$$
$$9-\frac{7}{9}\times \frac{7}{9}$$
$$9-\frac{7\times 7}{9\times 9}$$
$$9-\frac{49}{81}$$
$$\frac{729}{81}-\frac{49}{81}$$
$$\frac{729-49}{81}$$
$$\frac{680}{81}$$
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$\frac{2 ^ {3} \cdot 5 \cdot 17}{3 ^ {4}} = 8\frac{32}{81} = 8.395061728395062$
