[tex]a = 2^{59}-4^{29}-8^{19} = \\
= 2^{59}-(2^2)^{29}-(2^3)^{19} = \\
= 2^{59}-2^{2 \times 29}-2^{3 \times 19} = \\
= 2^{59}-2^{58}-2^{57} = 2^{57}(2^2 -2^1 -1) =2^{57}(4 -2 -1) = \boxed{2^{57}} \\ \\
b=3^{39}-2\times 9 \times 27^{12} = \\
=3^{39}-2\times 3^2 \times (3^3)^{12} = \\
=3^{39}-2\times 3^2 \times 3^{3\times12} = \\
=3^{39}-2\times 3^2 \times 3^{36} = \\
=3^{39}-2\times 3^{2+36} = \\
=3^{39}-2\times 3^{38} = 3^{38}(3-2)=\boxed{3^{38}}
[/tex]
[tex]\texttt{Comparam numerele: } a = 2^{57} \texttt{ si } b= 3^{38} \texttt{ :} \\ \\
a = 2^{57} = 2^{3 \times 19}=(2^3)^{19} = 8^{19} \\ \\
b = 3^{38} = 3^{2\times 19} = (3^2)^{19}=9^{19} \\ \\
8^{19} \ \textless \ 9^{19} \\ \\
\Longrightarrow ~~ \boxed{a \ \textless \ b}
[/tex]
