$(4\frac{23}{63} * 8\frac{37}{55} - 16\frac{1}{5} : \frac{21}{25}) * 14\frac{8}{11} : \frac{26}{77} * \frac{1}{405} = (\frac{63 * 4 + 23}{63} * \frac{55 * 8 + 37}{55} - \frac{5 * 16 + 1}{5} : \frac{21}{25}) * \frac{11 * 14 + 8}{11} : \frac{26}{77} * \frac{1}{405} = (\frac{63 * 4 + 23}{63} * \frac{55 * 8 + 37}{55} - \frac{5 * 16 + 1}{5} * \frac{25}{21}) * \frac{11 * 14 + 8}{11} * \frac{77}{26} * \frac{1}{405} = (\frac{252 + 23}{63} * \frac{440 + 37}{55} - \frac{80 + 1}{5} * \frac{5 * 5}{21}) * \frac{154 + 8}{11} * \frac{77}{26} * \frac{1}{405} = (\frac{275}{63} * \frac{477}{55} - \frac{81}{5} * \frac{5 * 5}{21}) * \frac{162}{11} * \frac{77}{26} * \frac{1}{405} = (\frac{55 * 5}{9 * 7} * \frac{53 * 9}{55} - \frac{3 * 3 * 9}{5} * \frac{5 * 5}{7 * 3}) * \frac{162}{11} * \frac{77}{26} * \frac{1}{405} = (\frac{5}{7} * \frac{53}{1} - \frac{3 * 9}{1} * \frac{5}{7}) * \frac{162}{11} * \frac{77}{26} * \frac{1}{405} = (53 - 27) * \frac{5}{7} * \frac{2 * 81}{11} * \frac{11 * 7}{26} * \frac{1}{81 * 5} = 26 * \frac{5}{7} * \frac{2 * 81}{11} * \frac{11 * 7}{26} * \frac{1}{81 * 5} = 2$