10. (4/3³ · 3/2²)⁶ : 4/3⁶.

10. $$ (\sqrt[4]{3^3} \cdot \sqrt[3]{2^2})^6 : \sqrt[4]{3^{36}} = (3^{\frac{3}{4}} \cdot 2^{\frac{2}{3}})^6 : 3^{\frac{36}{4}} = 3^{\frac{3}{4} \cdot 6} \cdot 2^{\frac{2}{3} \cdot 6} : 3^9 = 3^{\frac{18}{4}} \cdot 2^4 : 3^9 = 3^{\frac{9}{2}} \cdot 16 : 3^9 = 16 \cdot 3^{\frac{9}{2} - 9} = 16 \cdot 3^{-\frac{9}{2}} = \frac{16}{3^{\frac{9}{2}}} = \frac{16}{\sqrt{3^9}} = \frac{16}{\sqrt{3^8 \cdot 3}} = \frac{16}{3^4 \sqrt{3}} = \frac{16}{81 \sqrt{3}} = \frac{16 \sqrt{3}}{81 \cdot 3} = \frac{16 \sqrt{3}}{243} $$.

Ответ: $$\frac{16 \sqrt{3}}{243}$$