д) \(\frac{(5^2)^4 \cdot 25}{5^9} = \frac{5^{2 \cdot 4} \cdot 5^2}{5^9} = \frac{5^8 \cdot 5^2}{5^9} = \frac{5^{8+2}}{5^9} = \frac{5^{10}}{5^9} = 5^{10-9} = 5^1 = 5\)
e) \(\frac{(7^3)^3 \cdot 7^2}{(7^5)^2} = \frac{7^{3 \cdot 3} \cdot 7^2}{7^{5 \cdot 2}} = \frac{7^9 \cdot 7^2}{7^{10}} = \frac{7^{9+2}}{7^{10}} = \frac{7^{11}}{7^{10}} = 7^{11-10} = 7^1 = 7\)