5. Вычислите: 1) \(\frac{49^5 \cdot 7^{12}}{343^7}\); 2) \((\frac{4}{7})^6 \cdot (1\frac{3}{4})^4\).

1) \(\frac{49^5 \cdot 7^{12}}{343^7} = \frac{(7^2)^5 \cdot 7^{12}}{(7^3)^7} = \frac{7^{2 \cdot 5} \cdot 7^{12}}{7^{3 \cdot 7}} = \frac{7^{10} \cdot 7^{12}}{7^{21}} = \frac{7^{10+12}}{7^{21}} = \frac{7^{22}}{7^{21}} = 7^{22-21} = 7^1 = 7\)

Ответ: 7

2) \((\frac{4}{7})^6 \cdot (1\frac{3}{4})^4 = (\frac{4}{7})^6 \cdot (\frac{7}{4})^4 = \frac{4^6}{7^6} \cdot \frac{7^4}{4^4} = \frac{4^6 \cdot 7^4}{7^6 \cdot 4^4} = \frac{4^{6-4}}{7^{6-4}} = \frac{4^2}{7^2} = \frac{16}{49}\)

Ответ: \(\frac{16}{49}\)