The value of $$\frac{8}{9}{\text{ of}}\left( {5\frac{1}{4} \div 2\frac{1}{3}{\text{ of }}4} \right) \div \left( {8 \div \frac{2}{3}{\text{ of }}\frac{4}{5}} \right){\text{of}}\left( {8 \times \frac{2}{3} \div \frac{4}{5}} \right){\text{is:}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{8}{9}{\text{ of}}\left( {5\frac{1}{4} \div 2\frac{1}{3}{\text{ of }}4} \right) \div \left( {8 \div \frac{2}{3}{\text{ of }}\frac{4}{5}} \right){\text{of}}\left( {8 \times \frac{2}{3} \div \frac{4}{5}} \right) \cr & = \frac{8}{9}{\text{ of}}\left( {\frac{{21}}{4} \div \frac{7}{3} \times 4} \right) \div \left( {8 \div \frac{8}{{15}}} \right){\text{of}}\left( {8 \times \frac{2}{3} \times \frac{5}{4}} \right) \cr & = \frac{8}{9}{\text{ of}}\left( {\frac{{21}}{4} \times \frac{3}{{28}}} \right) \div \left( {8 \times \frac{{15}}{8}} \right){\text{of}}\left( {\frac{{20}}{3}} \right) \cr & = \left( {\frac{8}{9} \times \frac{9}{{16}}} \right) \div 100 \cr & = \frac{1}{{200}} \cr} $$