[tex]a)\\
\text{Le aducem pe toate la puterea 100.}\\\\
5^{300} = 5^{3\times100} = \Big(5^3\Big)^{100} =125^{100}\\\\
3^{400} = 3^4\times100 = \Big(3^4\Big)^{100} = 81^{100}\\\\
8^{200}=8^{2\times 100}= \Big(8^2\Big)^{100}=64^{100}\\\\
\text{Ordinea crescatoare este:}\\
64^{100};~81^{100};~125^{100}~~\Longleftrightarrow~~8^{200};~3^{400};~5^{300}[/tex]
[tex]b)\\
\text{Le aducem pe toate la puterea 15.}\\\\
2^{60} =2^{4\times 15} =\Big(2^4\Big)^{15} =16^{15} \\\\
3^{45} =3^{3\times 15} =\Big(3^3\Big)^{15} =27^{15} \\\\
5^{30}=5^{2\times 15} =\Big(5^2\Big)^{15} =25^{15} \\\\
\text{Ordinea crescatoare este:}\\
16^{15};~25^{15};~27^{15}~~\Longleftrightarrow~~2^{60};~5^{30};~3^{45} [/tex]
[tex]c)\\
\text{Le aducem pe toate la baza 2.}\\\\
32^{25}=\Big(2^5\Big)^{25}=2^{5\times25}=2^{125}\\\\
4^{62}=\Big(2^2\Big)^{62}=2^{2\times62}=2^{124} \\\\
64^{21}=\Big(2^6\Big)^{21}=2^{6\times21}= 2^{126}\\\\
\text{Ordinea crescatoare este:}\\
2^{124} ;~2^{125};~2^{126}~~\Longleftrightarrow~~4^{62};~32^{25};~64^{21}[/tex]
