jmc

Since division by $z$ is the same as multiplication by $\frac{1}{z}$, we are being asked to find $$x\cdot y\cdot \frac{1}{z}.$$Since $z=-\frac{11}{13}$, the reciprocal of $z$ is $\frac{1}{z}=-\frac{13}{11}$. So we get $$\left(-\frac{2}{3}\right)\left(\frac{5}{7}\right)\left(-\frac{13}{11}\right)=\frac{2\cdot 5\cdot 13}{3\cdot 7\cdot 11}=\boxed{\frac{130}{231}}.$$The final answer is positive, because two of the three numbers being multiplied are negative (and a negative number times a negative number is a positive number).