276. Найдите значение выражения:

Решение:

1. \( 9^{5} \cdot 9^{-7} = 9^{5+(-7)} = 9^{-2} = \frac{1}{9^{2}} = \frac{1}{81} \)
2. \( 10^{-8} \cdot 10^{12} = 10^{-8+12} = 10^{4} = 10000 \)
3. \( 3^{-18} : 3^{-21} = 3^{-18 - (-21)} = 3^{-18+21} = 3^{3} = 27 \)
4. \( 2^{-9} \cdot 2^{-12} : 2^{-22} = 2^{-9 + (-12) - (-22)} = 2^{-21+22} = 2^{1} = 2 \)
5. \( (17^{4})^{-12} \cdot (17^{-6})^{-8} = 17^{-48} \cdot 17^{48} = 17^{-48+48} = 17^{0} = 1 \)
6. \( \frac{6^{-5} \cdot (6^{3})^{4}}{(6^{-7})^{2} \cdot 6^{-3}} = \frac{6^{-5} \cdot 6^{12}}{6^{-14} \cdot 6^{-3}} = \frac{6^{-5+12}}{6^{-14-3}} = \frac{6^{7}}{6^{-17}} = 6^{7 - (-17)} = 6^{7+17} = 6^{24} \)
7. \( 3^{-3} \cdot \left(\frac{2}{3}\right)^{-3} = 3^{-3} \cdot \frac{2^{-3}}{3^{-3}} = 2^{-3} = \frac{1}{2^{3}} = \frac{1}{8} \)
8. \( \frac{14^{-5}}{7^{-5}} = \left(\frac{14}{7}\right)^{-5} = 2^{-5} = \frac{1}{2^{5}} = \frac{1}{32} \)