**Решение:**
1) \(\frac{7}{16} \cdot \frac{8}{49} = \frac{7 \cdot 8}{16 \cdot 49} = \frac{1 \cdot 1}{2 \cdot 7} = \frac{1}{14}\)
2) \(\frac{4}{9} \cdot \frac{7}{9} = \frac{4 \cdot 7}{9 \cdot 9} = \frac{28}{81}\)
3) \(\frac{56}{69} \cdot \frac{69}{77} = \frac{56 \cdot 69}{69 \cdot 77} = \frac{56}{77} = \frac{8 \cdot 7}{11 \cdot 7} = \frac{8}{11}\)
4) \(\frac{55}{72} \cdot \frac{40}{99} = \frac{55 \cdot 40}{72 \cdot 99} = \frac{5 \cdot 10}{9 \cdot 9} = \frac{50}{81}\)
**Ответ:**
1) \(\frac{1}{14}\); 2) \(\frac{28}{81}\); 3) \(\frac{8}{11}\); 4) \(\frac{50}{81}\)