| The value of\[\frac{{{3}^{12+n}}\times {{9}^{2n-7}}}{{{3}^{5n}}}\]is equal to |
A) \[\frac{1}{9}\]
B) \[\frac{1}{7}\]
C) \[\frac{1}{8}\]
D) \[\frac{1}{12}\]
Correct Answer: A
Solution :
| \[\frac{{{3}^{12\,\,+\,\,n}}\times {{9}^{2n\,\,-\,\,7}}}{{{3}^{5n}}}=\frac{{{3}^{12\,\,+\,\,n}}\times {{3}^{2\,\,(2n\,\,-\,\,7)}}}{{{3}^{5n}}}\] |
| \[=\frac{{{3}^{12\,\,+\,\,n}}\times {{3}^{4n\,\,-\,\,14}}}{{{3}^{5n}}}\] |
| \[=\frac{{{3}^{12\,\,+\,\,n\,\,+\,\,4n\,\,-\,\,14}}}{{{3}^{5n}}}\] |
| \[=\frac{{{3}^{5n\,\,-\,\,2}}}{{{3}^{5n}}}={{3}^{5n\,\,-\,\,2-5n}}\] |
| \[={{3}^{-\,\,2}}=\frac{1}{{{3}^{2}}}=\frac{1}{9}\] |
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