Step-by-step explanation:
[tex] {( - 2x {y}^{4} })^{4} [/tex]
[tex] = {( - 2)}^{4} \times {x}^{4} \times { {y}^{4} }^{4} [/tex]
[tex] = 16 {x}^{4} {y}^{16} [/tex]