44.
[tex]a) \ \frac{5^{3}\cdot5^{8}}{5^{11}:5^{2}} = \frac{5^{3+8}}{5^{11-2}} = \frac{5^{11}}{5^{9}} = 5^{11-9} = 5^{2} = 25[/tex]
[tex]b) \ \frac{0,25^{3}:0,5^{3}}{5^{3}} = (\frac{0,25:0,5}{5})^{3} = 0,1^{3} = 0,001[/tex]
[tex]c) \ (\frac{2}{5})^{3}:(-\frac{2}{5})^{2} =(\frac{2}{5})^{3}\cdot(\frac{2}{5})^{2} = (\frac{2}{5})^{3-2} = (\frac{2}{5})^{1} = \frac{2}{5}[/tex]
[tex]d) \ (0,1^{2})^{3}:0,1^{3} = 0,1^{6}:0,1^{3} = 0,1^{6-3} = 0,1^{3} = 0,001[/tex]
45.
[tex]a) \ \frac{2^{n+1}}{2^{n}} = 2^{n+1-n} = 2^{1} = 2[/tex]
[tex]b) \ 6^{m}\cdot6^{3-m} = 6^{m+3-m} = 6^{3} = 216[/tex]
[tex]c) \ \frac{10^{k+1}}{10^{k-1}} = 10^{k+1-(k-1)}=10^{k+1-k+1} = 10^{2} = 100[/tex]
[tex]d) \ \frac{3^{2n+2}}{3^{2n-1}} =3^{2n+2-(2n-1)} = 3^{2n+2-2n+1} = 3^{3} = 27[/tex]
