[tex](3^{\frac{1}{2}}\cdot3^{-1,25}:3^{\frac{3}{4}})^{\frac{4}{3}}=\\\\=(3^{\frac{1}{2}}\cdot3^{-\frac{125}{100}}:3^{\frac{3}{4}})^{\frac{4}{3}}=\\\\=(3^{\frac{2}{4}}\cdot3^{-\frac{5}{4}}:3^{\frac{3}{4}})^{\frac{4}{3}}=\\\\=(3^{\frac{2}{4}+(-\frac{5}{4})}:3^{\frac{3}{4}})^{\frac{4}{3}}=\\\\=(3^{-\frac{3}{4}}:3^{\frac{3}{4}})^{\frac{4}{3}} =\\\\=(3^{-\frac{3}{4}-\frac{3}{4}})^{\frac{4}{3}}=\\\\=(3^\frac{-6}{4}})^{\frac{4}{3}}=\\\\=3^{-\frac{6}{4}\cdot\frac{4}{3}}=\\\\=3^{-2} = (\frac{1}{3})^{2} = \frac{1}{9}[/tex]
Wyjaśnienie:
[tex]a^{m}\cdot a^{m} = a^{m+n}\\\\a^{m}:a^{n} = a^{m-n}\\\\(a^{m})^{n} = a^{m\cdot n}[/tex]
[tex]a^{-n} = (\frac{1}{a})^{n}[/tex]
