Question : Simplify the following.
$81^{\frac{3}{4}}+[(20 \div 5 \text { of } 3 \times 6)+\{(8 \div 24 \text { of } 3) \times 4\}-10 \div 5]-\left(\frac{1}{32}\right)^{-\frac{2}{5}}$
Option 1: $24 \frac{1}{4}$
Option 2: $21 \frac{1}{9}$
Option 3: $27 \frac{4}{5}$
Option 4: $29 \frac{4}{9}$
Correct Answer: $29 \frac{4}{9}$
Solution :
Given expression,
$81^{\frac{3}{4}}+[(20 \div 5 \text { of } 3 \times 6)+\{(8 \div 24 \text { of } 3) \times 4\}-10 \div 5]-\left(\frac{1}{32}\right)^{-\frac{2}{5}}$
= $(3^4)^{\frac{3}{4}}+[(\frac{20}{15}\times6)+\{(\frac{8}{72})\times4\}-\frac{10}{5}]-(\frac{1}{2^5})^{-\frac{2}{5}}$
= $3^3+[(4\times2)+\{\frac{4}{9}-2]-2^2$
= $27+[8+\frac49-2]-4$
= $27+6+\frac49-4$
= $29+\frac{4}{9}$
= $29\frac{4}{9}$
Hence, the correct answer is $29\frac{4}{9}$.
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