7. 15⁸ –––––––– 36 ⋅ 5⁷

Для решения данного задания необходимо разложить 15 и 36 на простые множители.

15 = 3 ⋅ 5

36 = 6 ⋅ 6 = 2 ⋅ 3 ⋅ 2 ⋅ 3 = 2² ⋅ 3²

Решение:

1. 15⁸ = (3 ⋅ 5)⁸ = 3⁸ ⋅ 5⁸
2. 36 ⋅ 5⁷ = 2² ⋅ 3² ⋅ 5⁷
3. (3⁸ ⋅ 5⁸) / (2² ⋅ 3² ⋅ 5⁷) = (3⁸ / 3²) ⋅ (5⁸ / 5⁷) / 2² = 3⁶ ⋅ 5 / 2² = 729 ⋅ 5 / 4 = 3645 / 4 = 911,25

Ответ: 911,25