$(16$ points$)$ Use the Chnin Rule to find $\frac{dw}{dt}$ for the function

$w=\frac{4x{e}^{2y}}{z^2},$

where

$x=5t3,$

$y=1-3t^2,$

$z=t^7.$

Note: You do not have to simplify your final answer once you have evaluated and substituted $t$ back in$.$