7) ((2 2/3)^3 : 28 4/9 - 75/96) \(\cdot\) 4,25 - 5/7

Решение:

7. Седьмой пример:

1. \( 2\frac{2}{3} = \frac{8}{3} \)
2. \( (\frac{8}{3})^3 = \frac{512}{27} \)
3. \( 28\frac{4}{9} = \frac{256}{9} \)
4. \( \frac{512}{27} : \frac{256}{9} = \frac{512}{27} \cdot \frac{9}{256} = 2 \cdot \frac{1}{3} = \frac{2}{3} \)
5. \( \frac{75}{96} = \frac{25}{32} \)
6. \( \frac{2}{3} - \frac{25}{32} = \frac{64 - 75}{96} = -\frac{11}{96} \)
7. \( 4,25 = 4\frac{1}{4} = \frac{17}{4} \)
8. \( -\frac{11}{96} \cdot \frac{17}{4} = -\frac{187}{384} \)
9. \( -\frac{187}{384} - \frac{5}{7} = \frac{-1309 - 1920}{2688} = -\frac{3229}{2688} \)

Ответ: -3229/2688