24 (в степени 5) / 4 (в степени 7) * на 81 (81 в знаменателе)

24^ (5) / (4^ (7) * 81) = ?

a = b * c = > a^n = (b * c) ^n = b^n * c^n

24^ (5) = (8 * 3) ^5 = (2^ (3) * 3) ^5;

(a^n) ^m = a^ (m * n)

(2^ (3) * 3) ^5 = (2^3) ^5 * 3^5 = 2^15 * 3^5;

4^ (7) * 81 = (2^2) ^7 * 3^4 = 2^ (2 * 7) * 3^4 = 2^14 * 3^4;

(a^n) / (a^m) = a^ (n - m)

24^ (5) / (4^ (7) * 81) = 2^15 * 3^5/2^14 * 3^4 = 2^ (15 - 14) * 3 (5 - 4) = 2^1 * 3^1 = 2 * 3 = 6

Ответ: 6.