| The greatest number among \[{{3}^{50}},\]\[{{4}^{40}},\]\[{{5}^{30}}\] and \[{{6}^{20}}\] is [SSC (CGL) Mains 2015] |
A) \[{{6}^{20}}\]
B) \[{{5}^{30}}\]
C) \[{{3}^{50}}\]
D) \[{{4}^{40}}\]
Correct Answer: D
Solution :
| \[{{3}^{50}}={{({{3}^{5}})}^{10}}={{(243)}^{10}}\]\[\Rightarrow \]\[{{4}^{40}}={{({{4}^{4}})}^{10}}={{(256)}^{10}}\] |
| \[{{5}^{30}}={{({{5}^{3}})}^{10}}={{(125)}^{10}}\]\[\Rightarrow \]\[{{6}^{20}}={{({{6}^{2}})}^{10}}={{(36)}^{10}}\] |
| \[\therefore \] Greatest number is \[{{4}^{40}}.\] |
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