277. Найдите значение выражения:

Решение:

1. \( 6^{-9} \cdot 6^{6} = 6^{-9+6} = 6^{-3} = \frac{1}{6^{3}} = \frac{1}{216} \)
2. \( 7^{-16} : 7^{-18} = 7^{-16 - (-18)} = 7^{-16+18} = 7^{2} = 49 \)
3. \( 5^{-7} : 5^{-6} \cdot 5^{3} = 5^{-7 - (-6) + 3} = 5^{-7+6+3} = 5^{2} = 25 \)
4. \( \frac{4^{-7} \cdot (4^{-5})^{3}}{(4^{-3})^{7}} = \frac{4^{-7} \cdot 4^{-15}}{4^{-21}} = \frac{4^{-7-15}}{4^{-21}} = \frac{4^{-22}}{4^{-21}} = 4^{-22 - (-21)} = 4^{-22+21} = 4^{-1} = \frac{1}{4} \)
5. \( 0.8^{-4} \cdot \left(1\frac{1}{4}\right)^{-4} = \left(\frac{4}{5}\right)^{-4} \cdot \left(\frac{5}{4}\right)^{-4} = \left(\frac{4}{5} \cdot \frac{5}{4}\right)^{-4} = 1^{-4} = 1 \)
6. \( \frac{11^{-2}}{22^{-2}} = \left(\frac{11}{22}\right)^{-2} = \left(\frac{1}{2}\right)^{-2} = 2^{2} = 4 \)