[tex]\frac{6^{20}\cdot(\frac{1}{3})^{20}\cdot0,5^{8}}{(-5)^{4}:(-2,5)^{4}\cdot0,25}=\frac{(6\cdot\frac{1}{3})^{20}\cdot(\frac{1}{2})^{8}}{(-5:(-2,5))^{4}\cdot\frac{25}{100}} =\frac{2^{20}\cdot(\frac{1}{2})^{8}}{2^{4}\cdot\frac{1}{4}} =\frac{2^{20}\cdot2^{-8}}{2^{4}\cdot2^{-2}} = \frac{2^{20-8}}{2^{4-2}} =\\\\= \frac{2^{12}}{2^{2}} = 2^{12-2} = 2^{10}[/tex]
Wykorzystano własności potęgowania:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\a^{n}\cdot b^{n} = (a\cdot b)^{n}\\\\a^{-n} = (\frac{1}{a})^{n}, \ \ dla \ a \neq 0[/tex]
