a)
[tex]a\cdot b = 3^{10}\cdot3^{4} = 3^{10+4} = 3^{14}\\\\c\cdot d = 3^{2}\cdot3^{5} = 3^{2+5} = 3^{7}\\\\\frac{3^{14}}{3^{7}} = 3^{14-7} = \boxed{3^{7}}[/tex]
b)
[tex]a\cdot b = 2^{5}\cdot2^{7} = 2^{5+7} = 2^{12}\\\\c\cdot d = 2^{4}\cdot2^{6} = 2^{4+6} = 2^{10}\\\\\frac{2^{12}}{2^{10}} = 2^{12-10} =\boxed{ 2^{2}}[/tex]
c)
[tex]a\cdot b = 7^{8}\cdot7^{2} = 7^{8+2} = 7^{10}\\\\c\cdot d = 7^{5}\cdot7} = 7^{5+1} = 7^{6}\\\\\frac{7^{10}}{7^{6}} = 7^{10-6} =\boxed{ 7^{4}}[/tex]
