[tex]a)\\3^{4}\cdot(81\cdot9^{-6})^{-1} = 3^{4}\cdot(3^{4}\cdot(3^{2})^{-6})^{-1} = 3^{4}\cdot(3^{4}\cdot3^{-12})^{-1} = 3^{4}\cdot(3^{-8})^{-1} = 3^{4}\cdot3^{8} = 3^{12}[/tex]
[tex]b)\\125^{3}\cdot0,2^{-7} = (5^{3})^{3}\cdot(\frac{2}{10})^{-7} = 5^{9}\cdot(\frac{1}{5})^{-7} = 5^{9}\cdot5^{7} = 5^{16}[/tex]
[tex]c)\\0,01\cdot16\cdot5^{4} = 0,16\cdot5^{4} = \frac{16}{100}\cdot5^{4} = \frac{4}{25}\cdot5^{4} = \frac{2^{2}}{5^{2}}\cdot5^{4} =2^{2}\cdot5^{2} = (2\cdot5)^{2} = 10^{2}[/tex]
[tex]d)\\2^{4}\cdot9^{2}\cdot36^{-5} = 2^{4}\cdot(3^{2})^{2}\cdot(6^{2})^{-5} =2^{4}\cdot3^{4}\cdot6^{-10} = 6^{4}\cdot6^{-10} = 6^{-6}[/tex]
[tex]e) \ 32^{-2}:(64^{3}\cdot(\frac{1}{2})^{-3}) = (2^{5})^{-2}:((2^{6})^{3}\cdot2^{3}) = 2^{-10}:(2^{18}\cdot2^{3}) = 2^{-10}:2^{21} = 2^{-31}[/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}\\\\(\frac{a}{b})^{-n} = (\frac{b}{a})^{n}[/tex]
