Вычислите: 1) \(3^{4} 3^{5}\) 2) \(3^{3} 3^{3}\) 3) \(\frac{6^{2} 6^{3} 6}{6^{2} 6^{2} 6}\) 4) \(\frac{2^{3} 5^{2} 11^{2} 6}{2^{1} 3^{2} 2^{7} 10^{2}}\)

Краткое пояснение:

Пошаговое решение:

1. 1) \(3^{4} \cdot 3^{5} = 3^{4+5} = 3^{9}\)
2. 2) \(3^{3} \cdot 3^{3} = 3^{3+3} = 3^{6}\)
3. 3) \(\frac{6^{2} \cdot 6^{3} \cdot 6^{1}}{6^{2} \cdot 6^{2} \cdot 6^{1}} = \frac{6^{2+3+1}}{6^{2+2+1}} = \frac{6^{6}}{6^{5}} = 6^{6-5} = 6^{1} = 6\)
4. 4) \(\frac{2^{3} \cdot 5^{2} \cdot 11^{2} \cdot 6}{2^{1} \cdot 3^{2} \cdot 2^{7} \cdot 10^{2}} = \frac{2^{3} \cdot 5^{2} \cdot 11^{2} \cdot (2 \cdot 3)}{2^{1} \cdot 3^{2} \cdot 2^{7} \cdot (2 \cdot 5)^{2}} = \frac{2^{3} \cdot 5^{2} \cdot 11^{2} \cdot 2^{1} \cdot 3^{1}}{2^{1} \cdot 3^{2} \cdot 2^{7} \cdot 2^{2} \cdot 5^{2}} = \frac{2^{3+1} \cdot 3^{1} \cdot 5^{2} \cdot 11^{2}}{2^{1+7+2} \cdot 3^{2} \cdot 5^{2}} = \frac{2^{4} \cdot 3^{1} \cdot 5^{2} \cdot 11^{2}}{2^{10} \cdot 3^{2} \cdot 5^{2}} = \frac{11^{2}}{2^{10-4} \cdot 3^{2-1}} = \frac{11^{2}}{2^{6} \cdot 3^{1}} = \frac{121}{64 \cdot 3} = \frac{121}{192}\)

Ответ: 1) $$3^{9}$$; 2) $$3^{6}$$; 3) $$6$$; 4) $$\frac{121}{192}$$