3. Выполните действия: 1) 0,5a³b⁴ · 3b⁵a² 2) -12m³n⁹ : 6m²n⁶ 3) (2x²c³)³ 4) ab² · (-2b⁴c⁸) 5) -25a⁵b⁴c² : 5a²b²c²

Решение:

1. \( 0.5a^3b^4 · 3b^5a^2 = (0.5 · 3) · (a^3 · a^2) · (b^4 · b^5) = 1.5 a^{3+2} b^{4+5} = 1.5a^5b^9 \)
2. \( -12m^3n^9 : 6m^2n^6 = \frac{-12m^3n^9}{6m^2n^6} = \frac{-12}{6} · \frac{m^3}{m^2} · \frac{n^9}{n^6} = -2 m^{3-2} n^{9-6} = -2mn^3 \)
3. \( (2x^2c^3)^3 = 2^3 · (x^2)^3 · (c^3)^3 = 8 x^{2·3} c^{3·3} = 8x^6c^9 \)
4. \( ab^2 · (-2b^4c^8) = (1 · -2) · a · (b^2 · b^4) · c^8 = -2 a b^{2+4} c^8 = -2ab^6c^8 \)
5. \( -25a^5b^4c^2 : 5a^2b^2c^2 = \frac{-25a^5b^4c^2}{5a^2b^2c^2} = \frac{-25}{5} · \frac{a^5}{a^2} · \frac{b^4}{b^2} · \frac{c^2}{c^2} = -5 a^{5-2} b^{4-2} c^{2-2} = -5 a^3 b^2 c^0 = -5a^3b^2 \)