281. Упростите выражение: 4) (0,2x⁷y⁸)³ ⋅ 6x²y²; 5) (-¹⁲ ab⁴)³ ⋅ (4a⁶)²; 6) (-²⁳ x²y)⁵ ⋅ (-³⁴ xy²)².

Решение:

1. \( (0.2x^7y^8)^3 \cdot 6x^2y^2 = 0.008x^{21}y^{24} \cdot 6x^2y^2 = 0.048x^{23}y^{26} \)
2. \( \left( -\frac{1}{2}ab^4 \right)^3 \cdot (4a^6)^2 = \left( -\frac{1}{8}a^3b^{12} \right) \cdot 16a^{12} = -2a^{15}b^{12} \)
3. \( \left( -\frac{2}{3}x^2y \right)^5 \cdot \left( -\frac{3}{4}xy^2 \right)^2 = \left( -\frac{32}{243}x^{10}y^5 \right) \cdot \left( \frac{9}{16}x^2y^4 \right) = \left( -\frac{32}{243} \cdot \frac{9}{16} \right) x^{12}y^9 = \left( -\frac{2}{27} \right) x^{12}y^9 = -\frac{2}{27}x^{12}y^9 \)

Ответ: 4) \( 0.048x^{23}y^{26} \); 5) \( -2a^{15}b^{12} \); 6) \( -\frac{2}{27}x^{12}y^9 \).