Question

Which of the following is the smallest?

3^3333
2^5555
6^2222
4^3333​

Answer 1

Answer:

the smallest digit is 2^5555

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following is the smallest

$\sf{1. \: \: {3}^{3333} }$

$\sf{2. \: \: {2}^{5555} }$

$\sf{3. \: \: {6}^{2222} }$

$\sf{4. \: \: {4}^{3333} }$

EVALUATION

Here the given numbers are

$\sf{ {3}^{3333} , {2}^{5555} , {6}^{2222} , {4}^{3333} }$

Now

$\sf{ {3}^{3333} = {( {3}^{3} )}^{1111} = {(27)}^{1111} }$

$\sf{ {2}^{5555} = {( {2}^{5} )}^{1111} = {(32)}^{1111} }$

$\sf{ {6}^{2222} = {( {6}^{2} )}^{1111} = {(36)}^{1111} }$

$\sf{ {4}^{3333} = {( {4}^{3} )}^{1111} = {(64)}^{1111} }$

Clearly

$\sf{64 < 36 < 32 < 27}$

$\sf{ \implies \: {(64)}^{1111} < {(36)}^{1111} < {(32)}^{1111} < {(27)}^{1111}}$

$\sf{ \implies \: {4}^{3333} < {6}^{2222} < {2}^{5555} < {3}^{3333}}$

So $\sf{ {3}^{3333}}$ is smallest

FINAL ANSWER

Hence the correct option is

$\sf{ 1. \: \: \: {3}^{3333}}$

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