Answer
$$\frac{d^4 x}{d t^4}|_{t=16}=\frac{3465}{256*2^{19}}$$
Work Step by Step
Since $=t^{-3/4}$, then
$$\frac{d x}{d t}=-\frac{3}{4}t^{-7/4}, \quad \frac{d^2 x}{d t^2}=\frac{21}{16}t^{-11/4}, \quad \frac{d^3 x}{d t^3}=-\frac{231}{64}t^{-15/4} $$
and we get $\frac{d^4 x}{d t^4}=\frac{3465}{256}t^{-19/4}$. Hence,
$$\frac{d^4 x}{d t^4}|_{t=16}=\frac{3465}{256*2^{19}}$$
