Найдите значение выражения √25а⁹ ⋅ √16b⁸ / √a⁵ b⁸ при a = 4 и b = 7

Источник варианта: СтатГрад

Решение:

√25а⁹ ⋅ √16b⁸ / √a⁵ b⁸ = √25 ⋅ √a⁵⁺⁴ ⋅ √16 ⋅ √b⁸ / √a⁵ ⋅ √b⁸ = 5 ⋅ √a⁵ ⋅ √a⁴ ⋅ 4 ⋅ √b⁸ / √a⁵ ⋅ √b⁸ = 5 ⋅ 1 ⋅ a² ⋅ 4 ⋅ 1 / 1 = 20a²

20 ⋅ 4² = 320

Ответ: 320