[tex] 2^{111} * 5^{38} =2^{3*37} * 5^{2*19}=( 2^{3} )^{37} * ( 5^{2} )^{19}=8^{37}*25^{19} [/tex]
si
[tex] 3^{131} = 3^{74+57} =3^{2*37}*3^{3*19}=( 3^{2} )^{37} * ( 3^{3} )^{19}=9^{37}*27^{19}[/tex]
Cum
[tex]8^{37}<9^{37}[/tex]
si
[tex]
25^{19}<27^{19}[/tex]
rezulta ca
[tex] 2^{111} * 5^{38} < 3^{131} [/tex]
