a) [tex]4^{31} = (2^{2})^{31} = 2^{62}[/tex]
[tex]8^{21} = (2^{3})^{21} = 2^{63}[/tex]
[tex]16^{15} = (2^{4})^{15} = 2^{60}[/tex]
[tex]=> 16^{15}, 4^{31}, 8^{21}.[/tex]
b) [tex]27^{13} = 3^{39}[/tex]
[tex]9^{18} = 3^{36}[/tex]
[tex]=> 9^{18}, 3^{37}, 27^{13}.[/tex]
c) [tex]8^{17} = 2^{51}[/tex]
[tex]32^{10} = 2^{50}[/tex]
[tex]=> 2^{48}, 32^{10}, 8^{17}.[/tex]
d) [tex]81^{11}=3^{44}[/tex]
[tex]9^{21}=3^{42}[/tex]
[tex]=> 3^{41}, 9^{21}, 81^{11}.[/tex]
