[tex](5^{3} )^{5} =5^{3\cdot 5} =5^{15} \\\\125^{6} =(5^{3} )^{6} =5^{3\cdot 6} =5^{18} \\\\5^{3^{2} } =5^{3\cdot 3} =5^{9} \\\\5^{2^{3} } =5^{2\cdot 2\cdot 2} =5^{8}\\\\\\5^{2^{3} } ~~ < ~~5^{3^{2} } ~~ < ~~(5^{3} )^{5} ~~ < ~~125^{6} \\\\czyli\\\\5^{8} ~~ < ~~5^{9} ~~ < ~~5^{15} ~~ < ~~5^{18}[/tex]
Korzystam ze wzoru:
[tex](x^{n} )^{m} =x^{n\cdot m}[/tex]
