1. Преобразуйте выражение: 1) a³ · a¹¹ 2) x⁻¹² · x⁵ 3) t⁻⁹ : t 4) y⁸ · y⁻⁸ 5) m⁷ : m³ 6) n⁻¹⁰ : n⁻⁴ 7) (s²)⁵ 8) (x⁻²)⁸ 9) (k⁻⁴)⁻⁶ 10) (x⁴y)⁻⁶ 11) (a⁻³/D)⁻²

1. Преобразуйте выражение:

1. \( a^3 \cdot a^{11} = a^{3+11} = a^{14} \)
2. \( x^{-12} \cdot x^5 = x^{-12+5} = x^{-7} = \frac{1}{x^7} \)
3. \( t^{-9} : t = t^{-9-1} = t^{-10} = \frac{1}{t^{10}} \)
4. \( y^8 \cdot y^{-8} = y^{8+(-8)} = y^0 = 1 \)
5. \( m^7 : m^3 = m^{7-3} = m^4 \)
6. \( n^{-10} : n^{-4} = n^{-10-(-4)} = n^{-10+4} = n^{-6} = \frac{1}{n^6} \)
7. \( (s^2)^5 = s^{2 \cdot 5} = s^{10} \)
8. \( (x^{-2})^8 = x^{-2 \cdot 8} = x^{-16} = \frac{1}{x^{16}} \)
9. \( (k^{-4})^{-6} = k^{(-4) \cdot (-6)} = k^{24} \)
10. \( (x^4y)^{-6} = x^{4 \cdot (-6)} y^{-6} = x^{-24} y^{-6} = \frac{1}{x^{24}y^6} \)
11. \( \left(\frac{a^{-3}}{D}\right)^{-2} = \frac{(a^{-3})^{-2}}{D^{-2}} = \frac{a^{(-3) \cdot (-2)}}{D^{-2}} = \frac{a^6}{D^{-2}} = a^6 D^2 \)