1. \(6^{-2} \cdot 6^3\) 2. \(3^{-5} : 3^{-5}\) 3. \(10^{-14} \cdot 10^{11} + 10^0\) 4. \(\left(\frac{3}{6}\right)^{-5} \cdot \left(\frac{6}{19}\right)^{-4}\) 5. \(10^{-5} : 100^3\) 6. \(3^7 : 3^9 : 3^{-2}\) 7. \(\frac{2^{24}}{(-2^{-3})^5 \cdot (-2)^{11}}\)

Решение:

1. \(6^{-2} \cdot 6^3 = 6^{-2+3} = 6^1 = 6\)
2. \(3^{-5} : 3^{-5} = 3^{-5 - (-5)} = 3^0 = 1\)
3. \(10^{-14} \cdot 10^{11} + 10^0 = 10^{-14+11} + 1 = 10^{-3} + 1 = \frac{1}{1000} + 1 = 1.001\)
4. \(\left(\frac{3}{6}\right)^{-5} \cdot \left(\frac{6}{19}\right)^{-4} = \left(\frac{1}{2}\right)^{-5} \cdot \left(\frac{6}{19}\right)^{-4} = 2^5 \cdot \left(\frac{19}{6}\right)^4 = 32 \cdot \frac{19^4}{6^4} = 32 \cdot \frac{130321}{1296} \approx 3216.14\)
5. \(10^{-5} : 100^3 = 10^{-5} : (10^2)^3 = 10^{-5} : 10^6 = 10^{-5-6} = 10^{-11}\)
6. \(3^7 : 3^9 : 3^{-2} = 3^{7-9} : 3^{-2} = 3^{-2} : 3^{-2} = 3^{-2 - (-2)} = 3^0 = 1\)
7. \(\frac{2^{24}}{(-2^{-3})^5 \cdot (-2)^{11}} = \frac{2^{24}}{(-1)^5 \cdot (2^{-3})^5 \cdot (-1)^{11} \cdot 2^{11}} = \frac{2^{24}}{-1 \cdot 2^{-15} \cdot -1 \cdot 2^{11}} = \frac{2^{24}}{2^{-15+11}} = \frac{2^{24}}{2^{-4}} = 2^{24 - (-4)} = 2^{28}\)

Ответ: 1. 6; 2. 1; 3. 1.001; 4. \(32 \cdot \left(\frac{19}{6}\right)^4\); 5. \(10^{-11}\); 6. 1; 7. \(2^{28}\).