Which number amongst 2^{40}, 3²1}, 4¹8} and 8¹2} is the smallest?

Correct Answer is : 3213²1}321

Correct Answer is : 3213²1}321

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UPSC Civil Services 2022 Prelims General Studies Paper II

Question : 9 of 80

Marks: +1, -0

2^{40}, 3^{21}, 4^{18}

8^{12}

Solution:

We have to find which is the smallest number among

2^{40}, 3^{21}, 4^{18}

and

8^{12}

8^{12}=(2^{3})^{12}=2^{36}

4^{18}=(2^{2})^{18}=2^{36}

2^{40}

3^{21}

So, in above expressions it is noted that (1.) and (2.) are equal and (3.) greater than (1.) and (2.).

So, the only option left which can be the smallest number is

3^{21}

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