Question Write \( \frac{\sqrt{h^{5}}}{\sqrt[6]{h^{11}}} \) as a single radical using the smallest possible root. Answer Attempt 1 out of 2 \( \sqrt[\square]{\square} \)

To simplify the expression \( \frac{\sqrt{h^{5}}}{\sqrt[6]{h^{11}}} \) into a single radical with the smallest possible root, follow these steps: 1. **Express Each Radical as an Exponent:** \[ \sqrt{h^5} = h^{\frac{5}{2}} \quad \text{and} \quad \sqrt[6]{h^{11}} = h^{\frac{11}{6}} \] 2. **Divide the Exponents:** \[ \frac{h^{\frac{5}{2}}}{h^{\frac{11}{6}}} = h^{\frac{5}{2} - \frac{11}{6}} \] 3. **Subtract the Exponents:** \[ \frac{5}{2} - \frac{11}{6} = \frac{15}{6} - \frac{11}{6} = \frac{4}{6} = \frac{2}{3} \] So, the expression simplifies to: \[ h^{\frac{2}{3}} \] 4. **Convert Back to Radical Form:** \[ h^{\frac{2}{3}} = \sqrt[3]{h^2} \] Thus, the simplified expression as a single radical with the smallest possible root is: \[ \sqrt[3]{h^2} \] **Answer:** \[ \sqrt[3]{h^{2}} \]