1. **State the problem:** Simplify the expression $$\frac{\sqrt{x^2 y z^3}}{\sqrt{x^2 y z^2}}$$ assuming $x, y, z > 0$. 2. **Use the property of square roots:** $$\frac{\sqrt{A}}{\sqrt{B}} = \sqrt{\frac{A}{B}}$$. 3. **Apply this to the expression:** $$\sqrt{\frac{x^2 y z^3}{x^2 y z^2}}$$ 4. **Simplify inside the square root:** $$\sqrt{\frac{\cancel{x^2} \cancel{y} z^3}{\cancel{x^2} \cancel{y} z^2}}} = \sqrt{z^{3-2}} = \sqrt{z}$$ 5. **Final simplified expression:** $$\sqrt{z}$$ 6. **Rewrite the original expression using the simplification:** Since the $x^2$ and $y$ terms cancel out, the original expression simplifies to $$\sqrt{z}$$ 7. **Check the options:** - $xy$ (no) - $\sqrt{xz}$ (no) - $x\sqrt{2}$ (no) - $x\sqrt{yz}$ (no) None of the options exactly match $\sqrt{z}$, but since the problem assumes $x,y,z>0$, and the simplification shows the expression equals $\sqrt{z}$, the closest equivalent is $\sqrt{z}$ alone. **Answer:** $\sqrt{z}$