[tex]1. \ \ 2\cdot2^{5}\cdot2^{11} = 2^{1+5+11} =\boxed{ 2^{17}}\\\\\underline{Odp. \ D}[/tex]
[tex]2. \ \ \frac{1}{4}\cdot2^{16} = \frac{1}{2^{2}}\cdot2^{16}} = \frac{2^{16}}{2^{2}} = 2^{16-2} = \boxed{2^{14}}\\\\\underline{Odp. \ B.}[/tex]
[tex]3.\\a) \ 5^{9}:5 = 5^{9-1} = 5^{8}\\\\b) \ (2,2)^{3}\cdot(2,2)^{3} = (2,2)^{3+3} = (2,2)^{6}\\\\c) \ \frac{7^{12}}{7^{10}} = 7^{12-10} = 7^{2}\\\\d) \ (-1\frac{1}{2})^{4}\cdot(-1\frac{1}{2})^{6} = (-1\frac{1}{2})^{4+6} = (-1\frac{1}{2})^{10}[/tex]
[tex]4. \ \ n = \frac{10^{15}}{10^{5}} = 10^{15-5} = 10^{10}[/tex]
Odp. Liczba 10¹⁵ jest 10¹⁰ razy większa od liczby 10⁵.
[tex]5. \ \frac{2^{4}\cdot2^{5}:2}{2^{3}\cdot2} = \frac{2^{4+5-1}}{2^{3+1}} = \frac{2^{8}}{2^{4}} = 2^{8-4} = 2^{4} = 16[/tex]
Wykorzystano własności potęg:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}[/tex]
