4. \( \left(4 p q^{4}\right)^{3} \)

Let's first expand \( \left(4 p q^{4}\right)^{3} \). When we raise a product of numbers and variables to a power, we distribute that power to each element inside the parentheses. Therefore, we have: \[ \left(4 p q^{4}\right)^{3} = 4^{3} \cdot p^{3} \cdot \left(q^{4}\right)^{3}. \] Calculating each part: - \( 4^{3} = 64 \), - \( p^{3} = p^{3} \), - \( \left(q^{4}\right)^{3} = q^{12} \). So, combining all parts, we get: \[ \left(4 p q^{4}\right)^{3} = 64 p^{3} q^{12}. \]