Выполнить действия: 1) 2xy² ⋅ (-3x²y³)²; 2) (\(\frac{2}{5}\)c³d²)³ ⋅ (\(-\frac{5}{8}\)c²d)²

Решение:

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

Ответ: 1) 18x⁵y⁸; 2) \(\frac{1}{40}\)c¹³d⁸.