[tex]\displaystyle{ (3^{4})^{7} : 9^{13} = 3^{28} : (3^{2})^{13} = 3^{28} : 3^{26} = 3^{2} = 9 }[/tex]
[tex]\displaystyle{ (2^{9})^{2} : 4^{9} = 2^{18} : (2^{2})^{9} = 2^{18} : 2^{18} = 1 }[/tex]
[tex]\displaystyle{ 8^{24} : 16^{18} = (2^{3})^{24} : (2^{4})^{18} = 2^{72} : 2^{72} = 1 }[/tex]
[tex]\displaystyle{ 125^{9} : 25^{13} = (5^{3})^{9} : (5^{2})^{13} = 5^{27} : 5^{26} = 5 }[/tex]
[tex]\displaystyle{ 81^{15} : 27^{20} = (3^{4})^{15} : (3^{3})^{20} = 3^{60} : 3^{60} = 1 }[/tex]
[tex]\displaystyle{ 8^{13^{2}} : 64^{84} = 8^{ 169} : 64^{84} = (2^{3})^{169} : (2^{6})^{84} = 2^{507} : 2^{504} = 2^{3} = 8}[/tex]
[tex]\displaystyle{ 3^{7^{2} }: 81^{12} = 3^{49} : (3^{4})^{12} = 3^{49} : 3^{48} = 3 }[/tex]
