1.
[tex]\frac{3^{12} : (3^{6} * 3^{3}) }{3^{2} }[/tex] [tex]= \frac{3^{12} : 3^{9} }{3^{2} }[/tex] [tex]= \frac{3^{3} }{3^{2} } = 3^{1} = 3[/tex]
2.
[tex]5^{8} * 5^{6} = 5^{14}[/tex]
3.
a) [tex]5^{9} * 5^{8} = 5^{17}[/tex]
b) [tex]9^{9} * 9 * 9^{9} = 9^{9} * 9^{1} * 9^{9} = 9^{19}\\[/tex]
c) [tex](1\frac{2}{9})^{11} : (1\frac{2}{9})^{4} = (\frac{11}{9})^{11} : (\frac{11}{9})^{4} = (\frac{11}{9})^{7}[/tex]
4.
a) [tex]8 * 2^{3} * 2^{5} = 2^{3} * 2^{3} * 2^{5} = 2^{11}[/tex]
b) [tex]81 * 3^{5} : 3^{3} = 3^{3} * 3^{5} : 3^{3} = 3^{8} : 3^{3} = 3^{5}[/tex]
