6.
[tex]\frac{2^{10}:(2^{2}\cdot2^{4})}{2^{3}} = \frac{2^{10}:2^{6}}{2^{3}} = \frac{2^{4}}{2^{3}} = 2[/tex]
7.
[tex]a) \ 4^{6} = (2^{2})^{6} = 2^{12}\\\\b) \ 32^{13} = (2^{5})^{13} = 2^{65}\\\\c) \ (8^{6})^{2} = ((2^{3})^{6})^{2}=2^{36}\\\\d) \ (16^{6})^{4}=((2^{4})^{6})^{4} = 2^{96}[/tex]
8.
[tex]5^{7}\cdot2^{7} = \boxed{10^{7}} : 10^{3} = \boxed{10^{4}} \cdot0,8^{4} =\boxed{ 8^{4}}:16^{4} = \boxed{0,5^{4}}[/tex]
9.
[tex]\frac{5^{8}}{16}\cdot\frac{2^{9}}{125} =\frac{5^{8}}{2^{4}}\cdot\frac{2^{9}}{5^{3}} =\frac{5^{8}}{5^{3}}\cdot\frac{2^{9}}{2^{4}} =5^{5}\cdot2^{5} = (5\cdot2)^{5} = 10^{5}[/tex]
10.
[tex]\frac{1}{4}\cdot16^{7} = \frac{(4^{2})^{7}}{4} = \frac{4^{14}}{4^{1}} = 4^{13}[/tex]
11.
[tex]1000 \ m \ to \ 10^{4} \ dm[/tex]
