Найдите значение выражения √25a¹⁹/a¹¹ при a = 2.

Источник: Ященко ОГЭ 2025 (36 вар.)

Решение:

√25a¹⁹/a¹¹ = √25 ⋅ a¹⁹ / a¹¹ = √25 ⋅ √a^19-11 = 5 ⋅ √a⁸ = 5 ⋅ √a^4⋅2 = 5 ⋅ √(a⁴)² = 5 ⋅ a⁴

√25a¹⁹/a¹¹ при a = 2

5 ⋅ a⁴ = 5 ⋅ 2⁴ = 5 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 80

Ответ: 80