280. Упростите выражение: 1) 2a³ ⋅ (-5a⁴b⁵)²; 2) (-x⁶y)³ ⋅ 11x⁴y⁵; 3) (-0,6a³b⁵c⁶)² ⋅ 3a²c⁸; 4) -1ⁱ⁳⁰ m⁴n⁹ ⋅ (-ⁱ⁷ mn³)²; 5) 1⁷ₙ x⁷y² ⋅ (³/₄ x²y⁹)⁴; 6) -(-2c²d⁵)⁷ ⋅ (-¹⁷ c⁴d⁵)⁴.

Решение:

1. \( 2a^3 \cdot \left( -5a^4b^5 \right)^2 = 2a^3 \cdot 25a^8b^{10} = 50a^{11}b^{10} \)
2. \( \left( -x^6y \right)^3 \cdot 11x^4y^5 = -x^{18}y^3 \cdot 11x^4y^5 = -11x^{22}y^8 \)
3. \( \left( -0.6a^3b^5c^6 \right)^2 \cdot 3a^2c^8 = 0.36a^6b^{10}c^{12} \cdot 3a^2c^8 = 1.08a^8b^{10}c^{20} \)
4. \( -\frac{1}{11}m^4n^9 \cdot \left( -\frac{1}{7}mn^3 \right)^2 = -\frac{1}{11}m^4n^9 \cdot \frac{1}{49}m^2n^6 = -\frac{1}{539}m^6n^{15} \)
5. \( 1\frac{7}{9}x^7y^2 \cdot \left( \frac{3}{4}x^2y^9 \right)^4 = \frac{16}{9}x^7y^2 \cdot \frac{81}{256}x^8y^{36} = \frac{16 \cdot 81}{9 \cdot 256}x^{15}y^{38} = \frac{1}{16}x^{15}y^{38} \)
6. \( -\left( -2c^2d^5 \right)^7 \cdot \left( -\frac{1}{2}c^4d^5 \right)^4 = -\left( -128c^{14}d^{35} \right) \cdot \left( \frac{1}{16}c^{16}d^{20} \right) = 128c^{14}d^{35} \cdot \frac{1}{16}c^{16}d^{20} = 8c^{30}d^{55} \)

Ответ: 1) \( 50a^{11}b^{10} \); 2) \( -11x^{22}y^8 \); 3) \( 1.08a^8b^{10}c^{20} \); 4) \( -\frac{1}{539}m^6n^{15} \); 5) \( \frac{1}{16}x^{15}y^{38} \); 6) \( 8c^{30}d^{55} \).