5. Запишите выражение в виде произведения степеней простых множителей и найдите его значение. 1) 6 ⋅ 21 ⋅ 14 = (2 ⋅ 3) ⋅ (3 ⋅ 7) ⋅ (2 ⋅ 7) = 2² ⋅ 3² ⋅ 7² = 1764 2) 12 ⋅ 15 ⋅ 4 = 3) 24 ⋅ 26 = 4) 33 ⋅ 77 ⋅ 11 ⋅ 15 = 5) 9 ⋅ 72 ⋅ 37 = 6) 35 ⋅ 17 ⋅ 34 =

Решение:

1. 12 ⋅ 15 ⋅ 4 = (2² ⋅ 3) ⋅ (3 ⋅ 5) ⋅ 2² = 2⁴ ⋅ 3² ⋅ 5 = 16 ⋅ 9 ⋅ 5 = 144 ⋅ 5 = 720
2. 24 ⋅ 26 = (2³ ⋅ 3) ⋅ (2 ⋅ 13) = 2⁴ ⋅ 3 ⋅ 13 = 16 ⋅ 3 ⋅ 13 = 48 ⋅ 13 = 624
3. 33 ⋅ 77 ⋅ 11 ⋅ 15 = (3 ⋅ 11) ⋅ (7 ⋅ 11) ⋅ 11 ⋅ (3 ⋅ 5) = 3² ⋅ 5 ⋅ 7 ⋅ 11³ = 9 ⋅ 5 ⋅ 7 ⋅ 1331 = 45 ⋅ 7 ⋅ 1331 = 315 ⋅ 1331 = 419115
4. 9 ⋅ 72 ⋅ 37 = 3² ⋅ (2³ ⋅ 3²) ⋅ 37 = 2³ ⋅ 3⁴ ⋅ 37 = 8 ⋅ 81 ⋅ 37 = 648 ⋅ 37 = 23976
5. 35 ⋅ 17 ⋅ 34 = (5 ⋅ 7) ⋅ 17 ⋅ (2 ⋅ 17) = 2 ⋅ 5 ⋅ 7 ⋅ 17² = 10 ⋅ 7 ⋅ 289 = 70 ⋅ 289 = 20230

Ответ: 1) 1764, 2) 720, 3) 624, 4) 419115, 5) 23976, 6) 20230.