[tex]\left(\frac{\sqrt[3]{7} \sqrt[4]{7}}{\sqrt[12]{7^5}}\right)^6 = \left(\frac{7^{\frac{1}{3}} 7^{\frac{1}{4}}}{7^{\frac{5}{12}}}\right)^6 = 7^{(1/3 + 1/4 - 5/12) 6} = 7^{(4/12 + 3/12 - 5/12) 6} = 7^{2/12 * 6} = 7^{2/2} = 7^1 = 7[/tex]
[tex]\left(\frac{\sqrt[3]{7} \sqrt[4]{7}}{\sqrt[12]{7^5}}\right)^6 = \left(\frac{7^{\frac{1}{3}} 7^{\frac{1}{4}}}{7^{\frac{5}{12}}}\right)^6 = 7^{(1/3 + 1/4 - 5/12) 6} = 7^{(4/12 + 3/12 - 5/12) 6} = 7^{2/12 * 6} = 7^{2/2} = 7^1 = 7[/tex]