1. The problem involves simplifying expressions with square roots and cube roots. 2. For the first expression $\sqrt{25} \sqrt{6}$, use the property $\sqrt{a} \sqrt{b} = \sqrt{ab}$. 3. Calculate $\sqrt{25} = 5$, so the expression becomes $5 \sqrt{6}$. 4. The second expression is $5 \sqrt{6}$, which is already simplified. 5. The third expression is $25 \sqrt{6}$, which is also simplified. 6. For the cube root expression $2 \sqrt[3]{-54}$, note that $2^3 = 8$. 7. We can write $2 \sqrt[3]{-54} = \sqrt[3]{8} \sqrt[3]{-54} = \sqrt[3]{8 \times -54} = \sqrt[3]{-432}$. 8. Simplify $\sqrt[3]{-432}$. Since $432 = 8 \times 54$, and $\sqrt[3]{8} = 2$, we get $\sqrt[3]{-432} = \sqrt[3]{-8 \times 54} = -2 \sqrt[3]{54}$. 9. For $\sqrt[3]{54}$, factor as $\sqrt[3]{27 \times 2} = 3 \sqrt[3]{2}$. 10. So $-2 \sqrt[3]{54} = -2 \times 3 \sqrt[3]{2} = -6 \sqrt[3]{2}$. 11. For the last expression $\sqrt[3]{252} k^5$, factor $252 = 36 \times 7 = 6^2 \times 7$. 12. Since $\sqrt[3]{252} = \sqrt[3]{36 \times 7} = \sqrt[3]{36} \sqrt[3]{7}$, and $36 = 6^2$, it cannot be simplified further inside the cube root. 13. So the expression remains $\sqrt[3]{252} k^5$. Final answers: - $\sqrt{25} \sqrt{6} = 5 \sqrt{6}$ - $5 \sqrt{6}$ (already simplified) - $25 \sqrt{6}$ (already simplified) - $2 \sqrt[3]{-54} = -6 \sqrt[3]{2}$ - $\sqrt[3]{252} k^5$ (simplified as is)