c: Đặt 111=a
=>222=2a; 777=7a
\(222^{777}=\left(2a\right)^{7a}=\left(128a^7\right)^{a}\)
\(777^{222}=\left(7a\right)^{2a}=\left(49a^2\right)^{a}\)
\(128a^7-49a^2=a^2\left(128a^5-49\right)=111^2\cdot\left(128\cdot111^5-49\right)>0\)
=>\(128a^7>49a^2\)
=>\(\left(128a^7\right)^{a}>\left(49a^2\right)^{a}\)
=>\(222^{777}>777^{222}\)
b: Đặt \(101=a\)
=>202=2a; 303=3a
\(202^{303}=\left(2a\right)^{3a}=\left(8a^3\right)^{a}\)
\(303^{202}=\left(3a\right)^{2a}=\left(9a^2\right)^{a}\)
\(8a^3-9a^2\)
\(=a^2\cdot\left(8a-9\right)\)
\(=101^2\left(8\cdot101-9\right)>0\)
=>\(8a^3>9a^2\)
=>\(\left(8a^3\right)^{a}>\left(9a^2\right)^{a}\)
=>\(202^{303}>303^{202}\)
