9.
[tex]a) \ \frac{1}{5}(\sqrt[3]{15})^{3} = \frac{1}{5}\cdot15 = \frac{15}{5} = 3\\\\\\b) \ 2\sqrt[3]{4}\cdot3(\sqrt[3]{4})^{3} =6\sqrt[3]{4}\cdot\sqrt[3]{4^{2}} = 6\sqrt[3]{4\cdot4^{2}} = 6\sqrt[3]{4^{3}} = 6\cdot4 = 24\\\\\\c) \ (-3\sqrt[3]{-5})^{2}\cdot\sqrt[3]{-5} = 9\sqrt[3]{(-5)^{2}}\cdot\sqrt[3]{-5} = 9\sqrt[3]{(-5)^{2}\cdot(-5)} = 9\sqrt[3]{(-5)^{3}} =\\\\= 9\cdot(-5) = -45[/tex]
10.
[tex]\frac{81}{8^{3}}\cdot\frac{2^{15}}{3^{16}} = \frac{3^{4}}{(2^{3})^{3}}\cdot\frac{2^{15}}{3^{16}} = \frac{3^{4}}{3^{16}}\cdot\frac{2^{15}}{2^{9}} = 3^{-12}\cdot2^{6} = (\frac{1}{3})^{12}\cdot2^{6} = (\frac{1}{3})^{6}\cdot(\frac{1}{3})^{6}\cdot2^{6} =\\\\=(\frac{1}{3}\cdot\frac{1}{3}\cdot2)^{6}=(\frac{2}{9})^{6}[/tex]
Z własności potęg:
[tex]a^{m}\cdot a^{n} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n[/tex]
