6.096. $\left\{\begin{array}{l}x^{2} y^{3}=16 \\ x^{3} y^{2}=2\end{array}\right.$
## Solution.

Dividing the first equation of the system by the second, we get $\frac{y}{x}=8, y=8 x$.

From the second equation of the system, we have $x^{3} \cdot 64 x^{2}=2, x^{5}=\frac{1}{32}$, from which $x=\frac{1}{2};$ then $y=4$.

Answer: $\left(\frac{1}{2} ; 4\right)$