\[\boxed{\text{447\ (447).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ x^{3} \cdot \left( x^{2} \right)^{5} = x^{3} \cdot x^{10} = x^{3 + 10} =\]
\[= x^{13}\]
\[\textbf{б)}\ \left( a^{3} \right)^{2} \cdot a^{5} = a^{6} \cdot a^{5} = a^{6 + 5} =\]
\[= a^{11}\]
\[\textbf{в)}\ \left( a^{2} \right)^{3} \cdot \left( a^{4} \right)^{2} = a^{6} \cdot a^{8} =\]
\[= a^{6 + 8} = a^{14}\]
\[\textbf{г)}\ \left( x^{2} \right)^{5} \cdot \left( x^{5} \right)^{2} = x^{10} \cdot x^{10} =\]
\[= x^{10 + 10} = x^{20}\]
\[\textbf{д)}\ \left( m^{2}m^{3} \right)^{4} = \left( m^{5} \right)^{4} = m^{5 \cdot 4} =\]
\[= m^{20}\]
\[\textbf{е)}\ \left( x^{4} \cdot x \right)^{2} = \left( x^{5} \right)^{2} = x^{5 \cdot 2} = x^{10}\]