SSC Quantitative Aptitude Number System and its Operations Question Bank Numbers and Their Principles (I)

The greatest number among \[{{3}^{50}},\] \[{{4}^{40}},\]\[{{5}^{30}}\]and \[{{6}^{20}}\]is [SSC CGL Tier II, 2015]

A) \[{{3}^{50}}\]

B) \[{{4}^{40}}\]

C) \[{{5}^{30}}\]

D) \[{{6}^{20}}\]

Correct Answer: B

Solution :

[b] \[{{3}^{50}},\]\[{{4}^{40}},\]\[{{5}^{30}},\]\[{{6}^{20}}\]

\[={{({{3}^{5}})}^{10}},\]\[{{({{4}^{4}})}^{10}},\]\[{{({{5}^{3}})}^{10}},\]\[{{({{6}^{2}})}^{10}}\]

\[={{(243)}^{10}},\]\[{{(256)}^{10}},\]\[{{(125)}^{10}},\]\[{{(36)}^{10}}\]

It is clear that \[{{4}^{40}}\] given above is the greatest number.