Odpowiedź:
[tex]a)\ \ 2^{82}:4^{40}=2^{82}:(2^2)^{40}=2^{82}:2^{80}=2^{82-80}=2^2=4\\\\\\b)\ \ \frac{18^4}{9^4}=(\frac{18}{9})^4=2^4=16\\\\\\c)\ \ \dfrac{2^{15}\cdot27^4}{6^1^5}=\dfrac{2^1^5\cdot(3^3)^4}{3^1^5\cdot2^1^5}=\dfrac{\not2^1^5\cdot3^1^2}{3^1^5\cdot\not2^1^5}=\dfrac{3^1^2}{3^1^5}=3^{12-15}=3^{-3}=(\frac{1}{3})^3=\frac{1}{27}\\\\\\d)\ \ (5^2)^3\cdot2^6=5^6\cdot2^6=(5\cdot2)^6=10^6=1000000[/tex]
[tex]e)\ \ 0,2^8\cdot25^4=(\frac{1}{5})^8\cdot(5^2)^4=5^{-8}\cdot5^8=5^{-8+8}=5^0=1\\\\\\f)\ \ 0,01^{12}\cdot100^9=(\frac{1}{100})^{12}\cdot(10^2)^9=((\frac{1}{10})^2)^{12}\cdot10^{18}=(\frac{1}{10})^{24}\cdot10^{18}=10^{-24}\cdot10^{18}=\\\\=10^{-24+18}=10^{-6}=(\frac{1}{10})^6=\frac{1}{1000000}[/tex]
