\[\boxed{\text{353\ (353).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\ \]
\[1)\ 3m^{2}n \cdot 0,4mn^{3} = 1,2m^{3}n^{4}.\]
\[2)\ 7\frac{1}{3}b^{3}c^{2} \cdot \frac{9}{11}a^{4}b^{5} =\]
\[= \frac{22}{3} \cdot \frac{9}{11} \cdot a^{4}b^{8}c^{2} =\]
\[3) - 5x^{4}y^{2}z^{8} \cdot \left( 0,8x^{6}y^{8}z^{2} \right) =\]
\[= - 5 \cdot 0,8 \cdot x^{10}y^{10}z^{10} =\]
\[= 4x^{10}y^{10}z^{10}.\]
\[4) - 5\frac{3}{7}abc \cdot 3,5a^{12}b^{10}c =\]
\[= - \frac{38}{7} \cdot \frac{35}{10} \cdot a^{13}b^{11}c^{2} =\]
\[= - 19a^{13}b^{11}c^{2}\text{.\ }\]