Mutiply then Simplify. (1) \( \sqrt[3]{60^{4}} \cdot \sqrt[3]{18 a} \) (2) \( \sqrt{35} \cdot \sqrt{21} \cdot \sqrt{18} \) (3) \( \sqrt[3]{36 m^{4} n^{5} p^{3}} \cdot \sqrt{6 m n^{2} p^{3}} \) \( (\sqrt{3}-4)(\sqrt{3}+4) \)

To solve the given expressions, let's tackle them one by one: (1) Calculation: \[ \sqrt[3]{60^4} \cdot \sqrt[3]{18a} = \sqrt[3]{60^4 \cdot 18a} = \sqrt[3]{(60^4 \cdot 18) a} \] To simplify \(60^4 \cdot 18\), we find \(60^4 = (2^2 \cdot 3 \cdot 5)^4 = 2^8 \cdot 3^4 \cdot 5^4\) and \(18 = 2 \cdot 3^2\). So, \(60^4 \cdot 18 = 2^9 \cdot 3^6 \cdot 5^4\). Simplifying this gives us \( = \sqrt[3]{2^9 \cdot 3^6 \cdot 5^4a} = 2^{3} \cdot 3^{2} \cdot 5^{\frac{4}{3}} \sqrt[3]{a} = 8 \cdot 9 \cdot 5^{\frac{4}{3}} \sqrt[3]{a} = 72 \cdot 5^{\frac{4}{3}} \sqrt[3]{a} = 72 \cdot 5^{1} \cdot \sqrt[3]{5} \cdot \sqrt[3]{a} = 360 \cdot \sqrt[3]{5a}. \] (2) Calculation: \[ \sqrt{35} \cdot \sqrt{21} \cdot \sqrt{18} = \sqrt{35 \cdot 21 \cdot 18} = \sqrt{(5 \cdot 7)(3 \cdot 7)(2 \cdot 9)} = \sqrt{5 \cdot 7^2 \cdot 3 \cdot 2 \cdot 9} \] Here we simplify \(9 = 3^2\), thus this equals: \( = \sqrt{(5 \cdot 2) (3^3)(7^2)} = \sqrt{10 \cdot 27 \cdot 49} = \sqrt{10} \cdot 21 = 21\sqrt{10}. \] (3) Calculation: \[ \sqrt[3]{36 m^4 n^5 p^3} \cdot \sqrt{6 m n^2 p^3} = \sqrt[3]{36} \cdot m^{\frac{4}{3}} \cdot n^{\frac{5}{3}} \cdot p^{1} \cdot \sqrt{6} \cdot m^{\frac{1}{2}} \cdot n^{1} \cdot p^{\frac{3}{2}}. \] For \( \sqrt[3]{36} = 6^{\frac{1}{3}}\) and \( \sqrt{6} = 6^{\frac{1}{2}}\). The total becomes: \(6^{\frac{1}{3} + \frac{1}{2}} m^{\frac{4}{3} + \frac{1}{2}} n^{\frac{5}{3} + 1} p^{\frac{3}{2} + 1}\). Converting to a common denominator, we get the answer of \(6^{\frac{5}{6}} m^{\frac{11}{6}} n^{\frac{8}{3}} p^{\frac{5}{2}}.\) (4) For the expression \((\sqrt{3}-4)(\sqrt{3}+4)\), we can use the difference of squares formula: \[ (\sqrt{3})^2 - 4^2 = 3 - 16 = -13. \] Combining all final results: 1) \(360\sqrt[3]{5a}\) 2) \(21\sqrt{10}\) 3) \(6^{\frac{5}{6}} m^{\frac{11}{6}} n^{\frac{8}{3}} p^{\frac{5}{2}}\) 4) \(-13\)