[tex]a)\\125^{12} = (5^{3})^{12} = 5^{36}, \ \ \ \ 25^{18} = (5^{2})^{18} = 5^{36}\\\\125^{12} = 25^{18}[/tex]
[tex]b)\\(\frac{1}{64})^{4} = ((\frac{1}{2})^{6})^{4} = (\frac{1}{2})^{24}, \ \ \ \ (\frac{1}{16})^{7}=((\frac{1}{2})^{4})^{7} = (\frac{1}{2})^{28}\\\\(\frac{1}{64})^{4}>(\frac{1}{16})^{7}[/tex]
[tex]c)\\0,0016^{9} = (0,2^{4})^{9} = 0,2^{36}, \ \ \ \ 0,008^{12} = (0,2^{3})^{12} =0,2^{36}\\\\0,0016^{9} = 0,008^{12}[/tex]
[tex]d)\\27^{160} = (3^{3})^{160} = 3^{480}, \ \ \ \ 81^{130}=(3^{4})^{130} = 3^{520}\\\\27^{160} < 81^{130}[/tex]
[tex]e)\\0,001^{9} = (0,1^{3})^{9} = 0,1^{27}, \ \ \ \ 0,01^{15} = (0,1^{2})^{15} = 0,1^{30}\\\\0,001^{9} > 0,01^{15}[/tex]
[tex]f)\\(\frac{27}{64})^{18} = ((\frac{3}{4})^{3})^{18} = (\frac{3}{4})^{54}, \ \ \ \ (\frac{9}{16})^{26} = ((\frac{3}{4})^{2})^{26} = (\frac{3}{4})^{52}\\\\(\frac{27}{64})^{18} < (\frac{9}{16})^{26}}[/tex]
