| Direction: What should come in place of question mark (?) in the following questions? |
A) \[{{(\sqrt{14})}^{4}}\]
B) \[{{(\sqrt{14})}^{8}}\]
C) \[{{(\sqrt{14})}^{7}}\]
D) \[{{(\sqrt{14})}^{5}}\]
E) \[{{(\sqrt{14})}^{6}}\]
Correct Answer: C
Solution :
\[{{(2744)}^{\frac{2}{3}}}\div {{(38416)}^{\frac{3}{4}}}\times ?={{(\sqrt{14})}^{5}}\] or, \[{{(14)}^{3\times \frac{2}{3}}}\div {{(14)}^{4\times \frac{3}{4}}}\times ?={{(\sqrt{14})}^{5}}\] or, \[{{(14)}^{2}}\div {{(14)}^{3}}\times ?={{(\sqrt{14})}^{5}}\] or, \[{{(14)}^{-1}}\times ?={{(\sqrt{14})}^{5}}\] \[\therefore \]\[?=14\times {{(\sqrt{14})}^{5}}={{(\sqrt{14})}^{7}}\]
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