[tex] \left[2^{ - 1} + \left( \frac{2}{5} \right) ^{ - 2} \right] : \left[(0,3444 \cdots)^{0} + \sqrt[3]{9^{1,5} } \right]. \left( \frac{3}{2} \right)^{ - 3} \\ \\ \left[ \frac{1}{2} + \left( \frac{5}{2} \right)^{2} \right] : \left[1+ 9^{ \frac{1,5}{3} } \right]. \left( \frac{2}{3} \right)^{ 3} \\ \\ \left[ \frac{1}{2} + \frac{25}{4} \right] : \left[1+ 9^{ \frac{1}{2} } \right]. \left(\frac{8}{27} \right) \\ \\ \left[ \frac{4 + 50}{8} \right] : \left[1+ 3 \right]. \left(\frac{8}{27} \right) \\ \\ \left[ \frac{ 54}{8} \right] : \left [4 \right]. \left(\frac{8}{27} \right) \\ \\ \left( \frac{54}{32} \right). \left( \frac{8}{27} \right) \\ \\ \frac{2}{4} \: \: \to \: \boxed{ \frac{1}{2} }[/tex]
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[tex] \left[2^{ - 1} + \left( \frac{2}{5} \right) ^{ - 2} \right] : \left[(0,3444 \cdots)^{0} + \sqrt[3]{9^{1,5} } \right]. \left( \frac{3}{2} \right)^{ - 3} \\ \\ \left[ \frac{1}{2} + \left( \frac{5}{2} \right)^{2} \right] : \left[1+ 9^{ \frac{1,5}{3} } \right]. \left( \frac{2}{3} \right)^{ 3} \\ \\ \left[ \frac{1}{2} + \frac{25}{4} \right] : \left[1+ 9^{ \frac{1}{2} } \right]. \left(\frac{8}{27} \right) \\ \\ \left[ \frac{4 + 50}{8} \right] : \left[1+ 3 \right]. \left(\frac{8}{27} \right) \\ \\ \left[ \frac{ 54}{8} \right] : \left [4 \right]. \left(\frac{8}{27} \right) \\ \\ \left( \frac{54}{32} \right). \left( \frac{8}{27} \right) \\ \\ \frac{2}{4} \: \: \to \: \boxed{ \frac{1}{2} }[/tex]