[tex]c) \ 2^{8}\cdot16^{4}:8^{2} = 2^{8}\cdot(2^{4})^{4}:(2^{3})^{2} = 2^{8}\cdot2^{16}:2^{6} = 2^{24}:2^{6} =2^{18}\\\\\\d) \ \frac{2\cdot3^{3}\cdot8^{5}}{16^{4}\cdot3} = \frac{2\cdot3^{8}\cdot(2^{3})^{5}}{(2^{4})^{4}\cdot3} = \frac{2\cdot3^{3}\cdot2^{15}}{2^{16}\cdot3} = \frac{2^{16}}{2^{16}}\cdot\frac{3^{3}}{3} = 1\cdot3^{2} = 3^{2}\\\\\\e) \ 3^{5}\cdot9^{4}\cdot27 =3^{5}\cdot(3^{2})^{4}\cdot3^{3} = 3^{5}\cdot3^{8}\cdot3^{3} = 3^{16}[/tex]
Wykorzystano własności potęg:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\(a^{m})^{n} = a^{m\cdot n}\\\\a^{m}:a^{n} = a^{m-n}[/tex]
