Simplify the following $${81^{\frac{3}{4}}} + \left[ {\left( {20 \div 5\,{\text{of }}3 \times 6} \right) + \left\{ {\left( {8 \div 24\,{\text{of }}3} \right) \times 4} \right\} - 10 \div 5} \right] - {\left( {\frac{1}{{32}}} \right)^{ - \frac{2}{5}}}$$

Solution (By Examveda Team)

$$\eqalign{ & {81^{\frac{3}{4}}} + \left[ {\left( {20 \div 5\,{\text{of }}3 \times 6} \right) + \left\{ {\left( {8 \div 24\,{\text{of }}3} \right) \times 4} \right\} - 10 \div 5} \right] - {\left( {\frac{1}{{32}}} \right)^{ - \frac{2}{5}}} \cr & = 27 + \left[ {\left( {20 \div 15 \times 6} \right) + \left\{ {\left( {8 \div 72} \right) \times 4} \right\} - 2} \right] - 4 \cr & = 27 + \left[ {8 + \frac{4}{9} - 2} \right] - 4 \cr & = 23 + \frac{{58}}{9} \cr & = \frac{{265}}{9} \cr & = 29\frac{4}{9} \cr} $$