270. Упростите выражение: 1) 12a² ⋅ 5a³b⁷; 2) −4m³ ⋅ 0,25m⁶; 3) 13c²d ⋅ (−3cd); 4) 56x⁵y¹⁴ ⋅ 2/7 x²y; 5) −3/20 p²q⁸ ⋅ 40/81 p⁸q²; 6) −6 1/2 mn⁸p¹¹ ⋅ 3 5/13 m³n⁵.

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Accepted Answer

$$12a^2 \cdot 5a^3b^7 = (12 \cdot 5) \cdot (a^2 \cdot a^3) \cdot b^7 = 60a^{2+3}b^7 = 60a^5b^7$$
$$-4m^3 \cdot 0,25m^6 = (-4 \cdot 0,25) \cdot (m^3 \cdot m^6) = -1 \cdot m^{3+6} = -m^9$$
$$13c^2d \cdot (-3cd) = (13 \cdot (-3)) \cdot (c^2 \cdot c) \cdot (d \cdot d) = -39c^{2+1}d^{1+1} = -39c^3d^2$$
$$56x^5y^{14} \cdot \frac{2}{7}x^2y = \frac{56 \cdot 2}{7} \cdot (x^5 \cdot x^2) \cdot (y^{14} \cdot y) = \frac{112}{7} x^{5+2} y^{14+1} = 16x^7y^{15}$$
$$-\frac{3}{20}p^2q^8 \cdot \frac{40}{81}p^8q^2 = -\frac{3 \cdot 40}{20 \cdot 81} \cdot (p^2 \cdot p^8) \cdot (q^8 \cdot q^2) = -\frac{120}{1620} p^{2+8} q^{8+2} = -\frac{2}{27}p^{10}q^{10}$$
$$-6\frac{1}{2}mn^8p^{11} \cdot 3\frac{5}{13}m^3n^5 = -\frac{13}{2}mn^8p^{11} \cdot \frac{44}{13}m^3n^5 = -\frac{13 \cdot 44}{2 \cdot 13} \cdot (m \cdot m^3) \cdot (n^8 \cdot n^5) \cdot p^{11} = -22m^{1+3}n^{8+5}p^{11} = -22m^4n^{13}p^{11}$$