smc

$x$ is negative, so we can just place a negative value into each expression and find the one that is positive. Suppose we use $-1$. $\text{(A)}\Rightarrow \frac{-1}{|-1|}=-1$ $\text{(B)}\Rightarrow -(-1{)}^2=-1$ $\text{(C)}\Rightarrow -2^{(-1)}=-\frac{1}{2}$ $\text{(D)}\Rightarrow -(-1{)}^{(-1)}=1$ $\text{(E)}\Rightarrow \sqrt[3]{-1}=-1$ Obviously only $\boxed{-x^{-1}}$ is positive.