Simplify : $$\frac{{343 \times 49}}{{216 \times 16 \times 81}} = ?$$

A. $$\frac{{{7^5}}}{{{6^7}}}$$

B. $$\frac{{{7^5}}}{{{6^8}}}$$

C. $$\frac{{{7^6}}}{{{6^7}}}$$

D. $$\frac{{{7^4}}}{{{6^8}}}$$

E. None of these

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & \frac{{343 \times 49}}{{216 \times 16 \times 81}} \cr & = \frac{{{7^3} \times {7^2}}}{{{6^3} \times {2^4} \times {3^4}}} \cr & = \frac{{{7^{\left( {3 + 2} \right)}}}}{{{6^3} \times {{\left( {2 \times 3} \right)}^4}}} \cr & = \frac{{{7^5}}}{{{6^3} \times {6^4}}} \cr & = \frac{{{7^5}}}{{{6^{\left( {3 + 4} \right)}}}} \cr & = \frac{{{7^5}}}{{{6^7}}} \cr} $$