15.
[tex]b) \ \dfrac{3^{8}:27\cdot9^{4}}{3^{2}\cdot81} = \dfrac{3^{8}:3^{3}\cdot(3^{2})^{4}}{3^{2}\cdot3^{4}} = \dfrac{3^{8}:3^{3}\cdot3^{8}}{3^{6}} = \dfrac{3^{5}\cdot3^{8}}{3^{6}} = \dfrac{3^{13}}{3^{6}} = 3^{7}[/tex]
[tex]d) \ (\dfrac{3}{2})^{4}\cdot(\dfrac{9}{4})^{3}:\dfrac{27}{8} = (\ddfrac{3}{2})^{4}\cdot((\dfrac{3}{2})^{2})^{3}:(\dfrac{3}{2})^{3} = (\dfrac{3}{3})^{4}\cdot(\dfrac{3}{2})^{6}:(\dfrac{3}{2})^{3} =(\dfrac{3}{2})^{10}:(\dfrac{3}{2})^{3}=\\\\=(\dfrac{3}{2})^{7}[/tex]
Wykorzystano własności potęg
[tex](a^{m})^{n} = a^{m\cdot n}\\\\a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}[/tex]
