[tex]\sqrt[3]{5}=5^{\frac{1}{3}}\\\\\sqrt[7]{25}=\sqrt[7]{5^2}=5^{\frac{2}{7}}\\\\\frac{1}{\sqrt[3]{5^3}}=\frac{1}{5}=5^{-1}\\\\5\cdot\sqrt[3]{5}=5^1\cdot5^{\frac{1}{3}}=5^{1+\frac{1}{3}}=5^{1\frac{1}{3}}=5^{\frac{4}{3}}\\\\\\Zastosowano\ \ wzory\\\\\sqrt[n]{a}=a^{\frac{1}{n}}\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\\sqrt[3]{a^3}=a\\\\a^m\cdot a^n=a^{m+n}\\\\\frac{1}{a^n}=a^{-n}[/tex]
