Вычислить: а) \(\frac{36^3}{216^2}\); б) \(\frac{2^5+96}{8^2+4^3}\); в) \(\frac{5^5\cdot35^2}{25^2\cdot42}\)

1. \[\frac{36^3}{216^2}=\frac{(6^2)^3}{(6^3)^2}=\frac{6^6}{6^6}=1.\]

2. \[\frac{2^5+96}{8^2+4^3}=\frac{32+96}{64+64}=\frac{128}{128}=1.\]

3. \[\frac{5^5\cdot35^2}{25^2\cdot42}=\frac{5^5\cdot(5\cdot7)^2}{(5^2)^2\cdot2\cdot3\cdot7}=\frac{5^7\cdot7^2}{5^4\cdot2\cdot3\cdot7}=\frac{5^3\cdot7}{6}=\frac{875}{6}.\]

Ответ: а) \(1\); б) \(1\); в) \(\frac{875}{6}\).