1.
[tex]A. \ 3^{5}\cdot3^{5} = 3^{10} = (3^{5})^{2}\\\\B. \ (2^{8})^{3} = (2^{3})^{8}\\\\C. \ (0,5)^{4} = (0,25)^{2}\\\\D. \ (3^{2})^{5} =3^{10} \neq 3^{2^{5}}=3^{32}\\\\Odp. \ D.[/tex]
2.
[tex]16^{5}:2^{5} = (16:2)^{5} = 8^{5}\\\\Odp. \ D.[/tex]
3.
[tex]9^{12} =(3^{2})^{12}=3^{24} = (3^{8})^{3} \\\\Odp. \ C.[/tex]
4.
[tex](2^{6})^{4} = 2^{24}\\\\32^{4} = (2^{5})^{4} = 2^{20}\\\\64^{5} = (2^{6})^{5} = 2^{30}\\\\4^{9} = (2^{2})^{9} = 2^{18}\\\\8^{9} = (2^{3})^{9} =2^{27}\\\\4^{9} < 32^{4} < (2^{6})^{4} < 8^{9} < 64^{5}[/tex]
5.
[tex]a = 7^{7}\\\\P = a^{2} = (7^{7})^{2} = 7^{14}[/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}:b^{n} = (a:b)^{n}[/tex]
