1. Найдите значение выражения: 610.66 α) (63)4.216 5 b) (72-51) + 3,6 : 92.

a) $$\frac{6^{10}\cdot 6^6}{(6^3)^4 \cdot 216} = \frac{6^{10+6}}{6^{3 \cdot 4} \cdot 6^3} = \frac{6^{16}}{6^{12} \cdot 6^3} = \frac{6^{16}}{6^{12+3}} = \frac{6^{16}}{6^{15}} = 6^{16-15} = 6^1 = 6$$

b) $$(72-51) \cdot \frac{5}{9} + 3,6 : 9^2 = 21 \cdot \frac{5}{9} + 3,6 : 81 = \frac{21}{1} \cdot \frac{5}{9} + \frac{36}{10} : \frac{81}{1} = \frac{7 \cdot 5}{3} + \frac{36}{10} \cdot \frac{1}{81} = \frac{35}{3} + \frac{4}{10} \cdot \frac{1}{9} = \frac{35}{3} + \frac{4}{90} = \frac{35}{3} + \frac{2}{45} = \frac{35 \cdot 15 + 2}{45} = \frac{525 + 2}{45} = \frac{527}{45} = 11\frac{32}{45}$$

Ответ: a) 6, b) $$\frac{527}{45} = 11\frac{32}{45}$$