[tex]\frac{(\frac{1}{27})^{3}:(3\sqrt{3})^{6}}{81^{-6}} = \frac{((\frac{1}{3})^{3})^{3}:3^{6}\cdot(3^{\frac{1}{2}})^{6}}{(3^{4})^{-6}} = \frac{(\frac{1}{3})^{9}:3^{6}\cdot3^{3}}{3^{-24}} =\frac{3^{-9}:3^{9}}{3^{-24}} = \frac{3^{-18}}{3^{-24}} = 3^{6} = (3^{2})^{3} =9^{3}[/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}\\\\(\frac{1}{a})^{n} =a^{-n} \ \ \ (dla \ \ a \neq 0)[/tex]
