5. Представьте в виде одночлена стандартного вида. 1) a) (4ac²)³ ⋅ (0,5a³c)²; 2) a) –(x²y⁴)⁴ ⋅ (6x⁴y)²; б) (\frac{2}{3}x²y³)³ ⋅ (-9x⁴y)²; б) (-10a³b²)⁵ ⋅ (-0,2a²b)⁵.

Ответ: 1) a) 8a⁵c⁸; б) -\frac{32}{3}x¹⁰y¹³; 2) a) -6x¹⁶y¹⁸; б) 32a²⁵b¹⁵

Решаем:

1. a) (4ac²)³ ⋅ (0,5a³c)² = 4³a³c⁶ * 0,5²a⁶c² = 64a³c⁶ * 0,25a⁶c² = 64 * 0,25 * a³ * a⁶ * c⁶ * c² = 16a⁹c⁸
2. б) (\frac{2}{3}x²y³)³ ⋅ (-9x⁴y)² = (\frac{2}{3})³x⁶y⁹ * (-9)²x⁸y² = \frac{8}{27}x⁶y⁹ * 81x⁸y² = \frac{8}{27} * 81 * x⁶ * x⁸ * y⁹ * y² = \frac{8 * 81}{27}x¹⁴y¹¹ = \frac{8 * 3}{1}x¹⁴y¹¹ = 24x¹⁴y¹¹
3. a) –(x²y⁴)⁴ ⋅ (6x⁴y)² = -x⁸y¹⁶ * 36x⁸y² = -36x¹⁶y¹⁸
4. б) (-10a³b²)⁵ ⋅ (-0,2a²b)⁵ = (-10)⁵a¹⁵b¹⁰ * (-0,2)⁵a¹⁰b⁵ = -100000a¹⁵b¹⁰ * -0,00032a¹⁰b⁵ = 3,2a²⁵b¹⁵

Ответ: 1) a) 8a⁵c⁸; б) -\frac{32}{3}x¹⁰y¹³; 2) a) -6x¹⁶y¹⁸; б) 32a²⁵b¹⁵