1. **Simplify \(\sqrt{125}\):** \(\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}\). 2. **Simplify \(\frac{9^{1/3}}{243^{1/3}}\):** Express bases as powers of 3: \(9 = 3^2\), \(243 = 3^5\). \(\frac{9^{1/3}}{243^{1/3}} = \frac{(3^2)^{1/3}}{(3^5)^{1/3}} = \frac{3^{2/3}}{3^{5/3}} = 3^{2/3 - 5/3} = 3^{-1} = \frac{1}{3}\). 3. **Simplify \(2^{3/2} \times \sqrt{2}\):** Recall \(\sqrt{2} = 2^{1/2}\). \(2^{3/2} \times 2^{1/2} = 2^{(3/2 + 1/2)} = 2^2 = 4\). 4. **Simplify \(\frac{5\sqrt{24} \div 2\sqrt{50}}{3\sqrt{3}}\):** First simplify numerator: \(5\sqrt{24} = 5 \times \sqrt{4 \times 6} = 5 \times 2\sqrt{6} = 10\sqrt{6}\), \(2\sqrt{50} = 2 \times \sqrt{25 \times 2} = 2 \times 5\sqrt{2} = 10\sqrt{2}\). So numerator: \(\frac{10\sqrt{6}}{10\sqrt{2}} = \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{\frac{6}{2}} = \sqrt{3}\). Denominator: \(3\sqrt{3}\). Whole expression: \(\frac{\sqrt{3}}{3\sqrt{3}} = \frac{1}{3}\). 5. **Simplify \(5^{-1})^3 \times 5^{5/4} \times \sqrt{25} \times (\sqrt[3]{125})^3\):** \((5^{-1})^3 = 5^{-3}\), \(\sqrt{25} = 5\), \((\sqrt[3]{125})^3 = 125 = 5^3\). Multiply all powers of 5: \(5^{-3} \times 5^{5/4} \times 5^{1} \times 5^{3} = 5^{-3 + 5/4 + 1 + 3} = 5^{(-3 + 1 + 3) + 5/4} = 5^{1 + 5/4} = 5^{9/4}\). 6. **Simplify \(3^{1/4} \times 27^{1/4}\):** Express 27 as \(3^3\): \(3^{1/4} \times (3^3)^{1/4} = 3^{1/4} \times 3^{3/4} = 3^{(1/4 + 3/4)} = 3^{1} = 3\). 7. **Simplify \(\sqrt{5} + 2\sqrt{6} -\):** The expression is incomplete; cannot simplify further. **Final answers:** \(a. 5\sqrt{5}\) \(b. \frac{1}{3}\) \(d. 4\) \(e. \frac{1}{3}\) \(g. 5^{9/4}\) \(i. 3\) \(j. \text{Incomplete expression}\)