3. Выполнить действия: 1) 2xy² ⋅ (-3x²y³)²; 2) (\(\frac{2}{5}c^3d^2\))³ ⋅ (-\(\frac{5}{8}c^2d\))²

Решение:

1. \( 2xy^2 \cdot (-3x^2y^3)^2 = 2xy^2 \cdot ((-3)^2 \cdot (x^2)^2 \cdot (y^3)^2) = 2xy^2 \cdot (9 \cdot x^4 \cdot y^6) = 2 \cdot 9 \cdot x^{1+4} \cdot y^{2+6} = 18x^5y^8 \)
2. \( (\frac{2}{5}c^3d^2)^3 \cdot (-\frac{5}{8}c^2d)^2 = (\frac{2^3}{5^3}c^{3 \cdot 3}d^{2 \cdot 3}) \cdot (\frac{(-5)^2}{8^2}c^{2 \cdot 2}d^2) = (\frac{8}{125}c^9d^6) \cdot (\frac{25}{64}c^4d^2) = \frac{8 \cdot 25}{125 \cdot 64} c^{9+4}d^{6+2} = \frac{200}{8000} c^{13}d^8 = \frac{1}{40}c^{13}d^8 \)

Ответ: 1) \(18x^5y^8\); 2) \(\frac{1}{40}c^{13}d^8\).