[tex]a) \ 2^{6}\cdot5^{7}=2^{6}\cdot5^{6}\cdot5=(2\cdot5)^{6}\cdot5=10^{6}\cdot5=\\\\=1000000\cdot5=5000000[/tex]
[tex]b) \ 0,2^{4}\cdot5^{7}=(\frac{2}{10})^{4}\cdot5^{7}=(\frac{1}{5})^{4}\cdot5^{7}=\frac{1}{5^{4}}\cdot5^{7}=\frac{5^{7}}{5^{4}}=5^{7-4}=5^{3}=125[/tex]
[tex]c) \ (\frac{2}{3})^{6}:(\frac{4}{9})^{5} = (\frac{2}{3})^{6}:((\frac{2}{3})^{2})^{5} = (\frac{2}{3})^{6}:(\frac{2}{3})^{2\cdot5} = (\frac{2}{3})^{6}:(\frac{2}{3})^{10} = \\\\=(\frac{2}{3})^{6-10}=(\frac{2}{3})^{-4}=(\frac{3}{2})^{4}=\frac{3^{4}}{2^{4}}=\frac{81}{16} =5\frac{1}{16}[/tex]
