$$\frac{35^6}{25^3 \\cdot 49^4} = \\frac{(5 \\cdot 7)^6}{(5^2)^3 \\cdot (7^2)^4} = \\frac{5^6 \\cdot 7^6}{5^6 \\cdot 7^8} = \\frac{1}{7^2} = \\frac{1}{49}$$
Ответ: $$\frac{1}{49}$$