[tex]a) \ 3^{6}:9 = 3^{6}:3^{2} = 3^{6-2} = 3^{4}\\\\b) \ 9\cdot3^{4} = 3^{2}\cdot3^{4} = 3^{2+4} = 3^{6}\\\\c) \ \frac{3^{7}}{9^{2}}=\frac{3^{7}}{(3^{2})^{2}} = \frac{3^{7}}{3^{4}} = 3^{7-4} = 3^{3}\\\\d) \ (3^{3})^{2} = 3^{3\cdot2} = 3^{6}\\\\e) \ \frac{27^{3}}{3^{8}} = \frac{(3^{3})^{3}}{3^{8}} = \frac{3^{9}}{3^{8}} = 3^{1}[/tex]
[tex]f) \ 9^{6}:3^{11} = (3^{2})^{6}:3^{11} = 3^{12}:3^{11} = 3^{1}\\\\g) \ \frac{9^{3}}{27} = \frac{(3^{2})^{3}}{3^{3}} = \frac{3^{6}}{3^{3}} = 3^{3}\\\\h) \ 3\cdot9\cdot27 = 3\cdot3^{2}\cdot3^{3} = 3^{6}[/tex]
Wykorzystane działania na potęgach:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n[/tex]
