Решение:

1. a) $$2^4 \cdot 5^4 = (2 \cdot 5)^4 = 10^4 = 10000$$
2. б) $$4^3 \cdot 25^3 = (4 \cdot 25)^3 = 100^3 = 1000000$$
3. в) $$0,25^{15} \cdot 4^{15} = (0,25 \cdot 4)^{15} = 1^{15} = 1$$
4. г) $$\left(\frac{2}{3}\right)^7 \cdot 1,5^7 = \left(\frac{2}{3} \cdot 1,5\right)^7 = \left(\frac{2}{3} \cdot \frac{3}{2}\right)^7 = 1^7 = 1$$
5. д) $$\left(\frac{5}{7}\right)^{10} \cdot 1,4^9 = \frac{5^{10}}{7^{10}} \cdot \left(\frac{14}{10}\right)^9 = \frac{5^{10}}{7^{10}} \cdot \frac{14^9}{10^9} = \frac{5^{10}}{7^{10}} \cdot \frac{(2 \cdot 7)^9}{(2 \cdot 5)^9} = \frac{5^{10}}{7^{10}} \cdot \frac{2^9 \cdot 7^9}{2^9 \cdot 5^9} = \frac{5^{10} \cdot 2^9 \cdot 7^9}{7^{10} \cdot 2^9 \cdot 5^9} = \frac{5}{7} = 0,(714285)$$ Приблизительно 0,71.
6. е) $$0,2^6 \cdot 50^7 = \left(\frac{1}{5}\right)^6 \cdot 50^7 = \frac{1}{5^6} \cdot 50^7 = \frac{50^7}{5^6} = \frac{(5^2 \cdot 2)^7}{5^6} = \frac{5^{14} \cdot 2^7}{5^6} = 5^8 \cdot 2^7 = 390625 \cdot 128 = 50000000$$

Ответ: a) 10000; б) 1000000; в) 1; г) 1; д) 5/7 ≈ 0,71; е) 50000000.