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Simplify : $$\frac{{16 \times 32}}{{9 \times 27 \times 81}} = ?$$

A. $${\left( {\frac{2}{3}} \right)^9}$$

B. $${\left( {\frac{2}{3}} \right)^{11}}$$

C. $${\left( {\frac{2}{3}} \right)^{12}}$$

D. $${\left( {\frac{2}{3}} \right)^{13}}$$

E. None of these

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & \frac{{16 \times 32}}{{9 \times 27 \times 81}} \cr & = \frac{{{2^4} \times {2^5}}}{{{3^2} \times {3^3} \times {3^4}}} \cr & = \frac{{{2^{\left( {4 + 5} \right)}}}}{{{3^{\left( {2 + 3 + 4} \right)}}}} \cr & = \frac{{{2^9}}}{{{3^9}}} \cr & = {\left( {\frac{2}{3}} \right)^9} \cr} $$

This Question Belongs to Arithmetic Ability >> Surds And Indices

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