[tex]\displaystyle\\
108^{72}\overset{?}{\ \textgreater \ =\ \textless \ }100^{108}\\\\
\text{Descompunem bazele:}\\\\
108=2^2\times3^3=\Big(3\sqrt[3]{4}\Big)^3 \\\\
100=2^2\times5^2=10^2\\\\
108^{72}=\left(\Big(3\sqrt[3]{4}\Big)^3\right)^{72}=\Big(3\sqrt[3]{4}\Big)^{3\times72}=\boxed{\Big(3\sqrt[3]{4}\Big)^{216}}\\\\
100^{108}=\Big(10^2\Big)^{108}=10^{2\times 108}=\boxed{10^{216}}\\\\
\text{Comparam numerele:} \\
3\sqrt[3]{4}~si~10 ~\Big|~~\text{(Ridicam la puterea a 3-a)}\\\\
\boxed{27\times4=108 \ \textless \ 1000 }[/tex]
[tex]\displaystyle\\
\Longrightarrow~~ \Big(3\sqrt[3]{4}\Big)^{216} \ \textless \ 10^{216}\\\\
\Longrightarrow~~ \boxed{108^{72} \ \textless \ 100^{108}}[/tex]