\[\boxed{\text{437\ (437).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ 2^{4} \cdot 5^{4} = (2 \cdot 5)^{4} = 10^{4} =\]
\[= 10\ 000\]
\[\textbf{б)}\ 4^{3} \cdot 25^{3} = (4 \cdot 25)^{3} = 100^{3} =\]
\[= 1\ 000\ 000\]
\[\textbf{в)}\ {0,25}^{15} \cdot 4^{15} = (0,25 \cdot 4)^{15} =\]
\[= 1^{15} = 1\]
\[\textbf{г)}\ \left( \frac{2}{3} \right)^{7} \cdot {1,5}^{7} = \left( \frac{2}{3} \cdot 1,5 \right)^{7} =\]
\[= 1^{7} = 1\]
\[\textbf{д)}\ \left( \frac{5}{7} \right)^{10} \cdot {1,4}^{9} = \frac{5}{7} \cdot \left( \frac{5}{7} \right)^{9} \cdot \left( \frac{7}{5} \right)^{9} =\]
\[= \frac{5}{7} \cdot \left( \frac{5}{7} \cdot \frac{7}{5} \right)^{9} = \frac{5}{7} \cdot 1^{9} = \frac{5}{7}\]
\[\textbf{е)}\ {0,2}^{6} \cdot 50^{7} = {0,2}^{6} \cdot 50^{6} \cdot 50 =\]
\[= (0,2 \cdot 50)^{6} \cdot 50 = 10^{6} \cdot 50 =\]
\[= 1\ 000\ 000 \cdot 50 = 50\ 000\ 000\ \]