Multiply, \[ 2 u \cdot 7 u^{4} x^{4} \cdot 3 x^{2} \] Simplify your answer as much as possible. \( \square \)

To solve the expression \( 2 u \cdot 7 u^{4} x^{4} \cdot 3 x^{2} \), we first multiply the coefficients and then the variables separately. 1. **Multiply the coefficients:** - \( 2 \cdot 7 \cdot 3 = 42 \) 2. **Multiply the variable \( u \):** - \( u \cdot u^{4} = u^{1 + 4} = u^{5} \) 3. **Multiply the variable \( x \):** - \( x^{4} \cdot x^{2} = x^{4 + 2} = x^{6} \) Now, combining everything together: \[ 2 u \cdot 7 u^{4} x^{4} \cdot 3 x^{2} = 42 u^{5} x^{6} \] The simplified expression is: \[ \boxed{42 u^{5} x^{6}} \]