8.
[tex]a) \ (5\sqrt[3]{4})^{3} -(6\sqrt{5})^{2} =5^{3}\cdot\sqrt[3]{4^{3}}-6^{2}\cdot\sqrt{5^{2}} = 125\cdot4 -36\cdot5 = 500-180 = 320\\\\\\b) \ (\sqrt[3]{7})^{3}-(\sqrt{3})^{2} = 7-3 = 4\\\\\\c) \ (\sqrt{12})^{2}+\sqrt[3]{13^{3}} = 12+13 = 25\\\\\\d) \ (2\sqrt[3]{4})^{3}+(3\sqrt{2})^{2} =2^{3}\cdot\sqrt[3]{4^{3}}+3^{2}\cdot\sqrt{2^{2}} = 8\cdot4+9\cdot2 = 32+18=50\\\\\\e) \ (10\sqrt[3]{5})^{3}-(5\sqrt{2})^{2} = 10^{3}\cdot\sqrt[3]{5^{3}}-5^{2}\cdot\sqrt{2^{2}} = 1000\cdot5-25\cdot2 = 5000-50 = 4950[/tex]
