A) 1
B) 3
C) 9
D) \[{{3}^{n}}\]
Correct Answer: C
Solution :
[c] \[\frac{{{(243)}^{\frac{n}{5}}}\times {{3}^{2n+1}}}{{{9}^{n}}\times {{3}^{n-1}}}=\frac{{{\left[ {{(3)}^{5}} \right]}^{\frac{n}{5}}}\times {{3}^{2n+1}}}{{{({{3}^{2}})}^{n}}\times {{3}^{n-1}}}\] \[=\frac{{{3}^{n}}\times {{3}^{2n+1}}}{{{3}^{2n}}\times {{3}^{n-1}}}\left[ {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \right]\] \[=\frac{{{3}^{3n+1}}}{{{3}^{3n-1}}}\,\,\,\,\,\,\,\left[ \frac{{{a}^{n}}}{{{a}^{m}}}={{a}^{n-m}} \right]\] \[={{3}^{2}}=9\]
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