| The value of \[\frac{(243)\times (243)}{(7)\times (49)\times (343)}\]is |
A) \[\frac{3}{7}\]
B) \[\frac{7}{3}\]
C) \[1\frac{3}{7}\]
D) \[2\frac{2}{7}\]
Correct Answer: A
Solution :
| \[\frac{{{(243)}^{0.13}}\times {{(243)}^{0.07}}}{{{7}^{0.25}}\times {{(49)}^{0.075}}\times {{(343)}^{0.2}}}=\frac{{{(243)}^{(0.13+0.07)}}}{{{7}^{0.25}}\times {{({{7}^{2}})}^{(0.075)}}\times {{({{7}^{3}})}^{0.2}}}\] \[=\,\,\frac{{{(243)}^{0.2}}}{{{7}^{0.25}}\times {{(7)}^{2\,\,\times \,}}^{0.075}\times {{(7)}^{3\,\,\times \,}}^{0.2}}\] |
| \[=\,\,\frac{{{({{3}^{5}})}^{0.2}}}{{{7}^{0.25}}\times {{7}^{0.15}}\times {{7}^{0.60}}}\] |
| \[=\,\,\frac{{{5}^{(5\,\times \,0.2)}}}{{{7}^{(0.25\,+\,0.15\,+\,0.6)}}}=\frac{{{3}^{1}}}{{{7}^{1}}}=\frac{3}{7}\] |
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