[tex]a)\\\\ 2^9*( \frac{1}{4})^9 : (\frac{1}{2})^5 = (\not {2}^1*\frac{1}{\not{4}^2})^9 : (\frac{1}{2})^5 =(\frac{1}{2})^9:(\frac{1}{2})^5=(\frac{1}{2})^{9-5}=(\frac{1}{2})^4=\frac{1}{16}\\\\b)\\\\\frac{( \frac{1}{5})^8:(\frac{2}{25})^8}{2,5^6}=\frac{( \frac{1}{5} :\frac{2}{25})^8}{ (\frac{25}{10})^6}=\frac{( \frac{1}{5} :\frac{2}{25})^8}{ (\frac{5}{2})^6} =\frac{( \frac{1}{\not{5}^1}*\frac{\not{5}^5}{2})^8}{ (\frac{5}{2})^6}=\frac{(\frac{5}{2})^8}{(\frac{5}{2})^6} =(\frac{5}{2})^{8-6}=(\frac{5}{2})^{2}=\\\\=\frac{25}{4}=6\frac{1}{4} \\\\stosujemy\ wzory:\\\\a^n*b^n=(a*b)^n\\\\a^n:a^m=a^{n-m}[/tex]
