1. **State the problem:** Simplify each radical expression using the given radical laws. 2. **Simplify each radical:** 1. $\sqrt[3]{250} = \sqrt[3]{125 \times 2} = \sqrt[3]{125} \times \sqrt[3]{2} = 5 \sqrt[3]{2}$ (using product rule and $\sqrt[3]{125}=5$) 2. $\sqrt{72m^{3}} = \sqrt{36 \times 2 \times m^{2} \times m} = \sqrt{36} \times \sqrt{m^{2}} \times \sqrt{2m} = 6m \sqrt{2m}$ 3. $\sqrt[3]{81^{3}} = 81$ (using same exponent-index rule for odd index: $\sqrt[3]{a^{3}}=a$) 4. $\sqrt[3]{125^{2}} = \left(\sqrt[3]{125}\right)^{2} = 5^{2} = 25$ (using power rule and $\sqrt[3]{125}=5$) 5. $\sqrt[3]{\frac{64}{125}} = \frac{\sqrt[3]{64}}{\sqrt[3]{125}} = \frac{4}{5}$ (using quotient rule and $\sqrt[3]{64}=4$, $\sqrt[3]{125}=5$) 6. $\sqrt[4]{\frac{32x^{6}}{81y^{8}}} = \frac{\sqrt[4]{32} \times \sqrt[4]{x^{6}}}{\sqrt[4]{81} \times \sqrt[4]{y^{8}}} = \frac{\sqrt[4]{16 \times 2} \times x^{6/4}}{3 \times y^{8/4}} = \frac{2 \sqrt[4]{2} \times x^{3/2}}{3 y^{2}}$ 7. $\sqrt[4]{(-8)^{4}} = | -8 | = 8$ (using same exponent-index rule for even index: $\sqrt[4]{a^{4}}=|a|$) 8. $\sqrt[5]{(-10)^{5}} = -10$ (using same exponent-index rule for odd index) 9. $\sqrt{256} = 16$ 10. $\sqrt[3]{\sqrt{25}} = \sqrt[3]{5} = 5^{1/3}$ (since $\sqrt{25}=5$) **Final answers:** 1. $5 \sqrt[3]{2}$ 2. $6m \sqrt{2m}$ 3. $81$ 4. $25$ 5. $\frac{4}{5}$ 6. $\frac{2 \sqrt[4]{2} x^{3/2}}{3 y^{2}}$ 7. $8$ 8. $-10$ 9. $16$ 10. $5^{1/3}$