Question

Which is greater between 10^414,
2^1242,6^828,8^621 ? (^ power sign)​

Answer 1

SOLUTION

TO DETERMINE

Greater between below :

$\sf{ {10}^{414} \: , \: {2}^{1242} \: ,\: {6}^{828} \: , \: {8}^{621} }$

EVALUATION

Here the given numbers are

$\sf{ {10}^{414} \: , \: {2}^{1242} \: ,\: {6}^{828} \: , \: {8}^{621} }$

We now simplify them

$\sf{ {10}^{414} = {10}^{2 \times 207} ={( {10}^{2})}^{207} = {100}^{207} }$

$\sf{{2}^{1242} = {2}^{6 \times 207} = {( {2}^{6}) }^{207} = {64}^{207} }$

$\sf{{6}^{828} = {6}^{4 \times 207} = {( {6}^{4}) }^{207} = {1296}^{207} }$

$\sf{{8}^{621} = {8}^{3 \times 207} = {( {8}^{3}) }^{207} = {512}^{207} }$

Now

1296 > 512 > 100 > 64

Hence the greater number is

$\sf{ {6}^{828} }$

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