[tex]A) \ (\frac{1}{81})^{5}\cdot27^{8} = (3^{-4})^{5}\cdot(3^{3})^{8} = 3^{-20}\cdot3^{24} = 3^{4}=81\\\\B) \ \frac{125^{7}}{25^{10}} = \frac{(5^{3})^{7}}{(5^{2})^{10}} = \frac{5^{21}}{5^{20}} = 5^{1} = 5\\\\C) \ 2^{5}\cdot4^{3}:8^{3} = 2^{5}\cdot(2^{2})^{3}:(2^{3})^{3} = 2^{5}\cdot2^{6}:2^{9} = 2^{11}:2^{9} = 2^{2} = 4\\\\H) \ 125^{5}:(25^{4}\cdot5^{6}) = (5^{3})^{5}:[(5^{2})^{4}\cdot5^{6}] = 5^{15}:(5^{8}\cdot5^{6}) = 5^{15}:5^{14} = 5^{1} = 5[/tex]
Wyjaśnienie:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n}\\\\a^{-n}=(\frac{1}{a})^{n}[/tex]
