Найдите значение выражения: 1. 6⁸ ⋅ 6⁻¹⁰; 2. 10⁻⁶ ⋅ 10⁹; 3. 3⁻¹⁷ : 3⁻²⁰; 4. 2⁻⁷ : 2 2⁻¹¹ : 2⁻¹⁸ 5. (19³)⁻⁷. (19⁻⁶)⁻⁵ 6. 9⁻⁵ ⋅ (9⁻²)⁶ (9⁻⁷)² ⋅ 9⁻²

1. Вычислим значения выражений:

1. 6⁸ ⋅ 6⁻¹⁰ = 6^{8 + (-10)} = 6^{8 - 10} = 6⁻² = 1/36
2. 10⁻⁶ ⋅ 10⁹ = 10^{-6 + 9} = 10³ = 1000
3. 3⁻¹⁷ : 3⁻²⁰ = 3^{-17 - (-20)} = 3^{-17 + 20} = 3³ = 27
4. 2⁻⁷ : 2^-11 : 2^-18 = 2^{-7 - (-11)} : 2^-18 = 2^{-7 + 11} : 2^-18 = 2⁴ : 2^-18 = 2^{4 - (-18)} = 2^{4 + 18} = 2²²
5. (19³)⁻⁷ = 19^3*(-7) = 19⁻²¹
6. (19⁻⁶)⁻⁵ = 19^-6*(-5) = 19³⁰
7. (19³⁻⁷) / (19⁻⁶)⁻⁵ = 19^-21 / 19³⁰ = 19^{-21 - 30} = 19⁻⁵¹
8. (9⁻⁵ ⋅ (9⁻²)⁶) / ((9⁻⁷)² ⋅ 9⁻²) = (9⁻⁵ ⋅ 9^-2*6) / (9^-7*2 ⋅ 9⁻²) = (9⁻⁵ ⋅ 9⁻¹²) / (9⁻¹⁴ ⋅ 9⁻²) = 9^{-5 + (-12)} / 9^{-14 + (-2)} = 9^-17 / 9^-16 = 9^{-17 - (-16)} = 9^{-17 + 16} = 9⁻¹ = 1/9