Calculate the following expression: \( (\frac{8}{27})^{-1} : \frac{12}{7} - (4\frac{3}{5} - \frac{6}{5}) \cdot 21 \) + \( (\frac{14}{5})^{-1} \cdot (-1.24) \cdot (1 - 1.56 - 99) \)

Решение:

1. Вычислим первое выражение: \( (\frac{8}{27})^{-1} = \frac{27}{8} \)
2. \( \frac{27}{8} : \frac{12}{7} = \frac{27}{8} \cdot \frac{7}{12} = \frac{9 \cdot 7}{8 \cdot 4} = \frac{63}{32} \)
3. \( 4\frac{3}{5} = \frac{23}{5} \)
4. \( \frac{23}{5} - \frac{6}{5} = \frac{17}{5} \)
5. \( \frac{17}{5} \cdot 21 = \frac{357}{5} \)
6. \( \frac{63}{32} - \frac{357}{5} = \frac{63 \cdot 5 - 357 \cdot 32}{32 \cdot 5} = \frac{315 - 11424}{160} = \frac{-11109}{160} \)
7. Вычислим второе выражение: \( (\frac{14}{5})^{-1} = \frac{5}{14} \)
8. \( \frac{5}{14} \cdot (-1.24) = \frac{5}{14} \cdot (-\frac{124}{100}) = \frac{5}{14} \cdot (-\frac{31}{25}) = \frac{1}{14} \cdot (-\frac{31}{5}) = -\frac{31}{70} \)
9. \( 1 - 1.56 - 99 = 1 - 100.56 = -99.56 \)
10. \( -\frac{31}{70} \cdot (-99.56) = \frac{31}{70} \cdot 99.56 = \frac{31}{70} \cdot \frac{9956}{100} = \frac{31}{70} \cdot \frac{2489}{25} = \frac{77159}{1750} \)
11. \( \frac{-11109}{160} + \frac{77159}{1750} = \frac{-11109 \cdot 1750 + 77159 \cdot 160}{160 \cdot 1750} = \frac{-19440750 + 12345440}{280000} = \frac{-7095310}{280000} = -\frac{709531}{28000} \)

Ответ: -\(\frac{709531}{28000}\).