Simplify;
[tex]\begin{gathered} (xy^3z^4)^4 \\ =x^4y^{12}z^{16} \end{gathered}[/tex]Each term in the parenthesis has its exponent multipled by that outside the parenthesis.
Hence you have x raised to power 1 times 4
y raised to power 3 times 4
z raised topower 4 times 4
The third option is the correct answer