1. **State the problem:** We need to find which expression is equivalent to $ (xy)^{\frac{9}{5}} $, where $x$ and $y$ are positive. 2. **Recall the exponent and root rules:** - $a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$ - For positive $x,y$, $(xy)^a = x^a y^a$ 3. **Apply the rules:** $$ (xy)^{\frac{9}{5}} = x^{\frac{9}{5}} y^{\frac{9}{5}} = \sqrt[5]{x^9 y^9} $$ 4. **Compare with options:** - A: $\sqrt[5]{x^9 y^9}$ matches exactly. - B: $\sqrt[9]{x^5 y^5}$ is $ (xy)^{\frac{5}{9}} $, not correct. - C: $\sqrt[14]{x^9 y^5}$ does not match the exponent or root. - D: $\sqrt[5]{x^5 y^5}$ is $ (xy)^1 $, not correct. **Final answer:** A