$ (\frac{5}{2})^{-4} \times (\frac{4}{9})^{3} \times (\frac{15}{4})^{2} \times (\frac{8}{27})^{-2} = (\frac{2}{5})^{4} \times (\frac{4}{9})^{3} \times (\frac{15}{4})^{2} \times (\frac{27}{8})^{8}=(\frac{2}{5})^{4} \times (\frac{2^2}{3^2})^{3} \times (\frac{3 \times 5}{2^2})^{2} \times (\frac{3^3}{2^3})^{2} = \\ \frac{2^4}{5^4} \times \frac{2^6}{3^6} \times \frac{3^2 \times 5^2}{2^4} \times \frac{3^6}{2^6} = \frac{2^{10} \times 3^8 \times 5^2}{2^10 \times 3^6 \times5^4} =\frac{3^2}{5^2} = \frac{9}{25} = \frac{36}{100}=0/36 $