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)
$$\eqalign{ & \frac{{343 \times 49}}{{216 \times 16 \times 81}} \cr & = \frac{{{7^3} \times {7^2}}}{{{6^3} \times {2^4} \times {3^4}}} \cr & = \frac{{{7^{\left( {3 + 2} \right)}}}}{{{6^3} \times {{\left( {2 \times 3} \right)}^4}}} \cr & = \frac{{{7^5}}}{{{6^3} \times {6^4}}} \cr & = \frac{{{7^5}}}{{{6^{\left( {3 + 4} \right)}}}} \cr & = \frac{{{7^5}}}{{{6^7}}} \cr} $$This Question Belongs to Arithmetic Ability >> Surds And Indices
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