1. \(\frac{7^{2}}{3^{5}}\)^2 2. \(\frac{5^{2}}{2^{5}}\)^2 3. \(\frac{8}{-b^{2}}\)^4 4. \(\frac{-7^{2}}{-3^{3}}\)^2

Решение:

Применяем свойство степени \( (a^m)^n = a^{m \cdot n} \) и \( (\frac{a}{b})^n = \frac{a^n}{b^n} \).

1. \( \left( \frac{7^2}{3^5} \right)^2 = \frac{(7^2)^2}{(3^5)^2} = \frac{7^{2 \cdot 2}}{3^{5 \cdot 2}} = \frac{7^4}{3^{10}} \)
2. \( \left( \frac{5^2}{2^5} \right)^2 = \frac{(5^2)^2}{(2^5)^2} = \frac{5^{2 \cdot 2}}{2^{5 \cdot 2}} = \frac{5^4}{2^{10}} \)
3. \( \left( \frac{8}{-b^2} \right)^4 = \frac{8^4}{(-b^2)^4} = \frac{8^4}{b^{2 \cdot 4}} = \frac{8^4}{b^8} \)
4. \( \left( \frac{-7^2}{-3^3} \right)^2 = \frac{(-7^2)^2}{(-3^3)^2} = \frac{7^{2 \cdot 2}}{3^{3 \cdot 2}} = \frac{7^4}{3^6} \)

Ответ: 1. \( \frac{7^4}{3^{10}} \); 2. \( \frac{5^4}{2^{10}} \); 3. \( \frac{8^4}{b^8} \); 4. \( \frac{7^4}{3^6} \).