3. Запишите выражение в виде произведения простых множителей и найдите его значение. 1) 2 ⋅ 6 ⋅ 14 ⋅ 22 = 2 ⋅ (2 ⋅ 3) ⋅ (2 ⋅ 7) ⋅ (2 ⋅ 11) = 3696 2) 2 ⋅ 3 ⋅ 35 ⋅ 4 = 3) 12 ⋅ 11 ⋅ 2 = 4) 3 ⋅ 3 ⋅ 5 ⋅ 11 ⋅ 15 = 5) 9 ⋅ 31 ⋅ 43 = 6) 5 ⋅ 17 ⋅ 58 ⋅ 22 =

Решение:

Разложим множители на простые и выполним умножение:

1. 2 ⋅ 3 ⋅ 35 ⋅ 4 = 2 ⋅ 3 ⋅ (5 ⋅ 7) ⋅ (2 ⋅ 2) = 2³ ⋅ 3 ⋅ 5 ⋅ 7 = 8 ⋅ 3 ⋅ 5 ⋅ 7 = 24 ⋅ 35 = 840
2. 12 ⋅ 11 ⋅ 2 = (2 ⋅ 2 ⋅ 3) ⋅ 11 ⋅ 2 = 2³ ⋅ 3 ⋅ 11 = 8 ⋅ 3 ⋅ 11 = 24 ⋅ 11 = 264
3. 3 ⋅ 3 ⋅ 5 ⋅ 11 ⋅ 15 = 3 ⋅ 3 ⋅ 5 ⋅ 11 ⋅ (3 ⋅ 5) = 3³ ⋅ 5² ⋅ 11 = 27 ⋅ 25 ⋅ 11 = 675 ⋅ 11 = 7425
4. 9 ⋅ 31 ⋅ 43 = (3 ⋅ 3) ⋅ 31 ⋅ 43 = 3² ⋅ 31 ⋅ 43 = 9 ⋅ 31 ⋅ 43 = 279 ⋅ 43 = 12000 - 279 = 11997
5. 5 ⋅ 17 ⋅ 58 ⋅ 22 = 5 ⋅ 17 ⋅ (2 ⋅ 29) ⋅ (2 ⋅ 11) = 2² ⋅ 5 ⋅ 11 ⋅ 17 ⋅ 29 = 4 ⋅ 5 ⋅ 11 ⋅ 17 ⋅ 29 = 20 ⋅ 11 ⋅ 17 ⋅ 29 = 220 ⋅ 17 ⋅ 29 = 3740 ⋅ 29 = 108460

Ответ: 2) 840, 3) 264, 4) 7425, 5) 11997, 6) 108460.