269. Выполните умножение одночленов:

Решение:

• 1) \[ (0.6a^4b^3) \cdot (4a^2b) = (0.6 \cdot 4) \cdot (a^4 \cdot a^2) \cdot (b^3 \cdot b) = 2.4a^{4+2}b^{3+1} = 2.4a^6b^4 \]
• 2) \[ (-2.8x^2y^5) \cdot (0.5x^4y^6) = (-2.8 \cdot 0.5) \cdot (x^2 \cdot x^4) \cdot (y^5 \cdot y^6) = -1.4x^{2+4}y^{5+6} = -1.4x^6y^{11} \]
• 3) \[ (13c^2d) \cdot (-3cd) = (13 \cdot -3) \cdot (c^2 \cdot c) \cdot (d \cdot d) = -39c^{2+1}d^{1+1} = -39c^3d^2 \]
• 4) \[ (0.7x^6y^9) \cdot (0.3xy) = (0.7 \cdot 0.3) \cdot (x^6 \cdot x) \cdot (y^9 \cdot y) = 0.21x^{6+1}y^{9+1} = 0.21x^7y^{10} \]
• 5) \[ \left(-\frac{3}{20}p^2q^8\right) \cdot \left(\frac{40}{81}p^8q^2\right) = \left(-\frac{3}{20} \cdot \frac{40}{81}\right) \cdot (p^2 \cdot p^8) \cdot (q^8 \cdot q^2) = \left(-\frac{3 \cdot 40}{20 \cdot 81}\right) \cdot p^{2+8}q^{8+2} = \left(-\frac{120}{1620}\right)p^{10}q^{10} = \left(-\frac{12}{162}\right)p^{10}q^{10} = \left(-\frac{2}{27}\right)p^{10}q^{10} \]
• 6) \[ \left(-6\frac{1}{2}mn^8p^{11}\right) \cdot \left(3\frac{5}{13}m^5n^5\right) = \left(-\frac{13}{2}mn^8p^{11}\right) \cdot \left(\frac{44}{13}m^5n^5\right) = \left(-\frac{13}{2} \cdot \frac{44}{13}\right) \cdot (m \cdot m^5) \cdot (n^8 \cdot n^5) \cdot p^{11} = \left(-\frac{44}{2}\right)m^{1+5}n^{8+5}p^{11} = -22m^6n^{13}p^{11} \]

Ответ: 1) 2.4a⁶b⁴; 2) -1.4x⁶y¹¹; 3) -39c³d²; 4) 0.21x⁷y¹⁰; 5) -2/27p¹⁰q¹⁰; 6) -22m⁶n¹³p¹¹