[tex]\it a = 2^{111}\cdot5^{38} =2^{108}\cdot2^3\cdot5^{36}\cdot5^2=(2^3)^{36}\cdot 5^{36}\cdot8\cdot25=
\\\;\\
=8^{36}\cdot5^{36}\cdot200= (8\cdot5)^{36}\cdot200 =40^{36} \cdot200= (40^2)^{18}\cdot200 =
\\\;\\
=1600^{18}\cdot200
\\\;\\
b= 3^{131} =3^{126}\cdot3^5=(3^7)^{18}\cdot243 =2187^{18}\cdot243
\\\;\\ \\\;\\
1600^{18}\cdot200 \ \textless \ 2187^{18}\cdot243 \Longrightarrow a\ \textless \ b.
[/tex]
