Aptitude Question ID: 107019

Find out the value of \frac{(243)^{0.13}\times (243)^{0.07}}{(7)^{0.25}\times (49)^{0.075}\times (343)^{0.2}} :
[A]\frac{7}{3}
[B]1\frac{3}{7}
[C]\frac{3}{7}
[D]2\frac{2}{7}

\mathbf{\frac{3}{7}}
Given Expression :
\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\times 7)^{0.075}\times (7\times 7\times 7)^{0.2}}
= \frac{\left ( 3^{5} \right )^{0.2}}{\left ( 7 \right )^{0.25}\times \left ( 7 \right )^{0.075\times 2}\times \left ( 7 \right )^{3\times 0.2}}
= \frac{(3)^{5\times 0.2}}{(7)^{0.25+0.15+0.6}} = \frac{3}{7}
Hence option [C] is correct answer.

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