64. Найдите значение выражения: 1) 29⋅39/67; 2) 187/26⋅96; 3) 79⋅58/358; 4) 29⋅514/507; 5) 1008/215⋅514; 6) 456/753

Решим каждое выражение по отдельности: 1) $$rac{2^9 cdot 3^9}{6^7} = rac{2^9 cdot 3^9}{(2 cdot 3)^7} = rac{2^9 cdot 3^9}{2^7 cdot 3^7} = 2^{9-7} cdot 3^{9-7} = 2^2 cdot 3^2 = 4 cdot 9 = 36$$ 2) $$rac{18^7}{2^6 cdot 9^6} = rac{(2 cdot 9)^7}{2^6 cdot 9^6} = rac{2^7 cdot 9^7}{2^6 cdot 9^6} = 2^{7-6} cdot 9^{7-6} = 2^1 cdot 9^1 = 2 cdot 9 = 18$$ 3) $$rac{7^9 cdot 5^8}{35^8} = rac{7^9 cdot 5^8}{(7 cdot 5)^8} = rac{7^9 cdot 5^8}{7^8 cdot 5^8} = 7^{9-8} cdot 5^{8-8} = 7^1 cdot 5^0 = 7 cdot 1 = 7$$ 4) $$rac{2^9 cdot 5^{14}}{50^7} = rac{2^9 cdot 5^{14}}{(2 cdot 25)^7} = rac{2^9 cdot 5^{14}}{(2 cdot 5^2)^7} = rac{2^9 cdot 5^{14}}{2^7 cdot (5^2)^7} = rac{2^9 cdot 5^{14}}{2^7 cdot 5^{14}} = 2^{9-7} cdot 5^{14-14} = 2^2 cdot 5^0 = 4 cdot 1 = 4$$ 5) $$rac{100^8}{2^{15} cdot 5^{14}} = rac{(10^2)^8}{2^{15} cdot 5^{14}} = rac{10^{16}}{2^{15} cdot 5^{14}} = rac{(2 cdot 5)^{16}}{2^{15} cdot 5^{14}} = rac{2^{16} cdot 5^{16}}{2^{15} cdot 5^{14}} = 2^{16-15} cdot 5^{16-14} = 2^1 cdot 5^2 = 2 cdot 25 = 50$$ 6) $$rac{45^6}{75^3} = rac{(9 cdot 5)^6}{(25 cdot 3)^3} = rac{9^6 cdot 5^6}{25^3 cdot 3^3} = rac{(3^2)^6 cdot 5^6}{(5^2)^3 cdot 3^3} = rac{3^{12} cdot 5^6}{5^6 cdot 3^3} = 3^{12-3} cdot 5^{6-6} = 3^9 cdot 5^0 = 3^9 cdot 1 = 19683 cdot 1 = 19683$$