a)
[tex](4\sqrt{5})^2-\sqrt{3}\cdot\sqrt{6}\cdot\sqrt{2}=4^2\cdot(\sqrt{5})^2-\sqrt{6}\cdot(\sqrt{3}\cdot\sqrt{2})=\\\\=16\cdot5-\sqrt{6}\cdot\sqrt{6}=80-(\sqrt{6})^2=80-6=\boxed{74}[/tex]
b)
[tex]\sqrt[3]{(7^3)^2}=\sqrt[3]{7^{3\cdot 2}}=\sqrt[3]{(7^2)^3}=7^2=\boxed{49}[/tex]
c)
[tex]\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=\sqrt{5^2}=\boxed{5}[/tex]
d)
[tex]\dfrac{\sqrt{15}}{\sqrt{2}}\cdot\dfrac{\sqrt{10}}{\sqrt{3}}=\sqrt{\dfrac{15\cdot10}{2\cdot3}}=\sqrt{\dfrac{5\cdot10}{2\cdot1}}=\sqrt{\dfrac{5\cdot5}{1\cdot1}}=\sqrt{5^2}=\boxed{5}[/tex]
