2. a) \( \frac{24^4}{4^4 \cdot 9^2} \) б) \( \frac{15^3}{25^2 \cdot 27} \) в) \( \frac{12^5}{4^3 \cdot 9^2} \) г) \( \frac{14^7}{4^4 \cdot 49^3} \)

Разбираемся:

a) \( \frac{24^4}{4^4 \cdot 9^2} = \frac{(4 \cdot 6)^4}{4^4 \cdot (3^2)^2} = \frac{4^4 \cdot 6^4}{4^4 \cdot 3^4} = \frac{6^4}{3^4} = (\frac{6}{3})^4 = 2^4 = 16 \)

б) \( \frac{15^3}{25^2 \cdot 27} = \frac{(3 \cdot 5)^3}{(5^2)^2 \cdot 3^3} = \frac{3^3 \cdot 5^3}{5^4 \cdot 3^3} = \frac{5^3}{5^4} = \frac{1}{5} = 0,2 \)

в) \( \frac{12^5}{4^3 \cdot 9^2} = \frac{(4 \cdot 3)^5}{4^3 \cdot (3^2)^2} = \frac{4^5 \cdot 3^5}{4^3 \cdot 3^4} = 4^2 \cdot 3 = 16 \cdot 3 = 48 \)

г) \( \frac{14^7}{4^4 \cdot 49^3} = \frac{(2 \cdot 7)^7}{(2^2)^4 \cdot (7^2)^3} = \frac{2^7 \cdot 7^7}{2^8 \cdot 7^6} = \frac{2^7 \cdot 7^7}{2^8 \cdot 7^6} = \frac{7}{2} = 3,5 \)