$\text{a)}\left(-6\sqrt{0,54}+15\sqrt{0,06}\right):\sqrt{6}=-6\sqrt{0,54}:\sqrt{6}+15\sqrt{0,06}:\sqrt{6}=$

$=-6\sqrt{0,54:6}+15\sqrt{0,06:6}=-6\sqrt{0,09}+15\sqrt{0,01}=$   

$=-6\cdot 0,3+15\cdot 0,1=-1,8+1,5=-0,3$  

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$\text{b)}\left(6\sqrt[3]{40\frac{1}{2}}-8\sqrt[3]{12}\right):\left(2\sqrt[3]{1,5}\right)=\left(6\sqrt[3]{40\frac{1}{2}}\right):\left(2\sqrt[3]{1,5}\right)-\left(8\sqrt[3]{12}\right):\left(2\sqrt[3]{1,5}\right)=$  

$=3\sqrt[3]{\frac{81}{2}:\frac{3}{2}}-4\sqrt[3]{12:\frac{3}{2}}=3\sqrt[3]{\frac{81}{2}\cdot \frac{2}{3}}-4\sqrt[3]{12\cdot \frac{2}{3}}=$

$=3\sqrt[3]{27}-4\sqrt[3]{8}=3\cdot 3-4\cdot 2=9-8=1$