| The value of \[\frac{{{(8.1)}^{3.6}}\times {{(9)}^{2.7}}}{{{(81)}^{4.2}}\times (3)}\]is [SSC (CGL) 2012] |
A) 3
B) 6
C) 9
D) 8.2
Correct Answer: C
Solution :
| \[\frac{{{(81)}^{3.6}}\times {{(9)}^{2.7}}}{{{(81)}^{4.2}}\times 3}=\frac{{{({{3}^{4}})}^{3.6}}\times {{({{3}^{2}})}^{2.7}}}{{{({{3}^{4}})}^{4.2}}\times 3}\] |
| \[=\frac{{{3}^{14.4}}\times {{3}^{5.4}}}{{{3}^{16.6}}\times {{3}^{1}}}={{3}^{14.4\,\,+\,\,5.4\,\,-\,\,16.8-1}}\] |
| \[\left[ \begin{align} & \because {{a}^{m}}\times {{a}^{n}}={{(a)}^{m+n}} \\ & {{a}^{m}}\div {{a}^{n}}={{(a)}^{m-n}} \\ \end{align} \right]\] |
| \[={{3}^{19.8-17.8}}={{3}^{2}}=9\] |
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