Simplify. \[ \left(3 y^{3} z^{4}\right)^{4}\left(2 x^{3} y z^{2}\right) \]

To simplify the expression \(\left(3 y^{3} z^{4}\right)^{4}\left(2 x^{3} y z^{2}\right)\), we start by simplifying each part separately. 1. **Simplifying \(\left(3 y^{3} z^{4}\right)^{4}\)**: \[ \left(3 y^{3} z^{4}\right)^{4} = 3^{4} (y^{3})^{4} (z^{4})^{4} \] Calculating each part: \[ 3^{4} = 81, \quad (y^{3})^{4} = y^{12}, \quad (z^{4})^{4} = z^{16} \] Therefore, \[ \left(3 y^{3} z^{4}\right)^{4} = 81 y^{12} z^{16} \] 2. **Now simplifying the product with \(\left(2 x^{3} y z^{2}\right)\)**: \[ 81 y^{12} z^{16} \cdot (2 x^{3} y z^{2}) = 81 \cdot 2 \cdot (y^{12} \cdot y) \cdot (z^{16} \cdot z^{2}) \cdot x^{3} \] Simplifying each part: \[ 81 \cdot 2 = 162 \] For the \(y\) terms: \[ y^{12} \cdot y = y^{13} \] For the \(z\) terms: \[ z^{16} \cdot z^{2} = z^{18} \] Putting it all together, we have: \[ 162 x^{3} y^{13} z^{18} \] Thus, the simplified expression is: \[ \boxed{162 x^{3} y^{13} z^{18}} \]