[tex]a) \ (5^{4})^{7} = 5^{4\cdot7} = 5^{28}\\\\b) \ 7^{15}:7^{9} = 7^{15-9} = 7^{6}\\\\c) \ 3^{12}\cdot3^{9} = 3^{12+9} = 3^{21}\\\\d) \ \frac{6^{10}\cdot6^{12}}{(6^{5})^{4}}=\frac{6^{22}}{6^{20}}= 6^{2}\\\\e) \ 8^{4}:2^{7} = (2^{3})^{4}:2^{7} = 2^{12}:2^{7} =2^{5}\\\\f) \ 81\cdot(3^{6})^{4} = 3^{4}\cdot3^{24} = 3^{28}[/tex]
[tex]g) \ 16^{7}:8^{7} = (16:8)^{7} = 2^{7}\\\\h) \ \frac{(5^{6})^{4}\cdot16^{5}}{125^{7}\cdot(2^{3})^{4}} = \frac{5^{24}\cdot(2^{4})^{5}}{(5^{3})^{7}\cdot2^{12}} = \frac{5^{24}\cdot2^{20}}{5^{21}\cdot2^{12}} = 5^{3}\cdot2^{8}[/tex]
