Решение:

1. $$\sqrt{27} \cdot \sqrt{3} = \sqrt{27 \cdot 3} = \sqrt{81} = 9$$
2. $$\sqrt{50} \cdot \sqrt{2} = \sqrt{50 \cdot 2} = \sqrt{100} = 10$$
3. $$\sqrt{160} \cdot \sqrt{250} = \sqrt{160 \cdot 250} = \sqrt{40000} = 200$$
4. $$\sqrt{0.1} \cdot \sqrt{0.4} = \sqrt{0.1 \cdot 0.4} = \sqrt{0.04} = 0.2$$
5. $$\frac{\sqrt{108}}{\sqrt{3}} = \sqrt{\frac{108}{3}} = \sqrt{36} = 6$$
6. $$\frac{\sqrt{90}}{\sqrt{0.016}} = \sqrt{\frac{90}{0.016}} = \sqrt{\frac{90000}{1.6}} = \sqrt{\frac{900000}{16}} = \frac{\sqrt{900000}}{\sqrt{16}} = \frac{100 \cdot \sqrt{90}}{4} = 25 \cdot \sqrt{90} = 25 \cdot \sqrt{9 \cdot 10} = 25 \cdot 3 \cdot \sqrt{10} = 75\sqrt{10}$$

Ответ: 1) 9; 2) 10; 3) 200; 4) 0.2; 5) 6; 6) $$75\sqrt{10}$$.