\[\boxed{\mathbf{820}\mathbf{.}}\]
\[1)\ f(x) = (2x - 3)^{5} \bullet \left( 3x^{2} + 2x + 1 \right)\]
\[= (2x - 3)^{4} \bullet \left( 42x^{2} + 6x + 4 \right).\]
\[2)\ f(x) = (x - 1)^{4} \bullet (x + 1)^{7}\]
\[= (x - 1)^{3} \bullet (x + 1)^{6} \bullet (11x - 3).\]
\[3)\ f(x) = \sqrt[4]{3x + 2} \bullet (3x - 1)^{4}\]
\[= \frac{3(3x - 1)^{3} \bullet (51x + 31)}{4\sqrt[4]{(3x + 2)^{3}}}.\]
\[4)\ f(x) = \sqrt[3]{2x + 1} \bullet (2x - 3)^{3}\]