[tex](\frac{\sqrt[3]{7}*\sqrt[4]{7} }{\sqrt[12]{7^{5} } } )^{6}[/tex]

= [tex](\frac{7^{\frac{1}{3}*7^{\frac{1}{4} } } }{7^{\frac{5}{12} } } )^{6} = (\frac{7^{\frac{1}{3}+\frac{1}{4} } }{7^{\frac{5}{12} } } )^{6} = (\frac{7^{\frac{7}{12} } }{7^{\frac{5}{12} } } )^{6} = (7^{\frac{7}{12}} / 7^{\frac{5}{12} } } )^{6} = (7^{\frac{7}{12}-\frac{5}{12} } )^{6} = (7^{\frac{1}{6} } )^{6}=7^{\frac{1}{6}*6}=7^{1} =7[/tex]