1) 37 ⋅ 117/336; 2) 286/75 ⋅ 45; 3) 58 ⋅ 95/455; 4) 316 ⋅ 210/545; 5) 365/29 ⋅ 38; 6) 184/125;

1) $$ \frac{3^7 \cdot 11^7}{33^6} = \frac{3^7 \cdot 11^7}{(3 \cdot 11)^6} = \frac{3^7 \cdot 11^7}{3^6 \cdot 11^6} = 3^{(7-6)} \cdot 11^{(7-6)} = 3^1 \cdot 11^1 = 3 \cdot 11 = 33$$

2) $$ \frac{28^6}{7^5 \cdot 4^5} = \frac{(7 \cdot 4)^6}{7^5 \cdot 4^5} = \frac{7^6 \cdot 4^6}{7^5 \cdot 4^5} = 7^{(6-5)} \cdot 4^{(6-5)} = 7 \cdot 4 = 28$$

3) $$ \frac{5^8 \cdot 9^5}{45^5} = \frac{5^8 \cdot (3^2)^5}{(5 \cdot 3^2)^5} = \frac{5^8 \cdot 3^{10}}{5^5 \cdot 3^{10}} = 5^{(8-5)} \cdot 3^{(10-10)} = 5^3 \cdot 3^0 = 5^3 \cdot 1 = 125 \cdot 1 = 125$$

4) $$ \frac{3^{16} \cdot 2^{10}}{54^5} = \frac{3^{16} \cdot 2^{10}}{(2 \cdot 3^3)^5} = \frac{3^{16} \cdot 2^{10}}{2^5 \cdot 3^{15}} = 3^{(16-15)} \cdot 2^{(10-5)} = 3 \cdot 2^5 = 3 \cdot 32 = 96$$

5) $$ \frac{36^5}{2^9 \cdot 3^8} = \frac{(4 \cdot 9)^5}{2^9 \cdot 3^8} = \frac{(2^2 \cdot 3^2)^5}{2^9 \cdot 3^8} = \frac{2^{10} \cdot 3^{10}}{2^9 \cdot 3^8} = 2^{(10-9)} \cdot 3^{(10-8)} = 2 \cdot 3^2 = 2 \cdot 9 = 18$$

6) $$ \frac{18^4}{12^5} = \frac{(2 \cdot 9)^4}{(3 \cdot 4)^5} = \frac{(2 \cdot 3^2)^4}{(3 \cdot 2^2)^5} = \frac{2^4 \cdot 3^8}{3^5 \cdot 2^{10}} = 3^{(8-5)} \cdot 2^{(4-10)} = 3^3 \cdot 2^{-6} = \frac{3^3}{2^6} = \frac{27}{64}$$

Ответ: 1) 33; 2) 28; 3) 125; 4) 96; 5) 18; 6) 27/64