[tex]a)\ \ \sqrt{7^3}=(7^3)^{\frac{1}{2}}=7^{\frac{3}{2}}\\\\\\b)\ \ \sqrt[3]{7^2}=(7^2)^{\frac{1}{3}}=7^{\frac{2}{3}}\\\\\\c)\ \ \frac{1}{\sqrt{7}}=(\sqrt{7})^{-1}=(7^{\frac{1}{2}})^{-1}=7^{-\frac{1}{2}}\\\\\\d)\ \ \frac{1}{\sqrt[3]{7}}=(\sqrt[3]{7})^{-1}=(7^{\frac{1}{3}})^{-1}=7^{-\frac{1}{3}}\\\\\\e)\ \ \sqrt{\frac{1}{7^3}}=\sqrt{7^{-3}}=(7^{-3})^{\frac{1}{2}}=7^{-\frac{3}{2}}[/tex]
[tex]f)\ \ \frac{1}{\sqrt[5]{7^3}}=(\sqrt[5]{7^3})^{-1}=(7^{\frac{3}{5}})^{-1}=7^{-\frac{3}{5}}\\\\\\g)\ \ 49\sqrt{7}=7^2\cdot7^{\frac{1}{2}}=7^{2+\frac{1}{2}}=7^{2\frac{1}{2}}=7^{\frac{5}{2}}\\\\\\h)\ \ 7\cdot\sqrt[5]{7}=7^1\cdot7^{\frac{1}{5}}=7^{1+\frac{1}{5}}=7^{1\frac{1}{5}}=7^{\frac{6}{5}}[/tex]
[tex]Zastosowano\ \ wzory\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\(a^m)^n=a^{m\cdot n}\\\\\frac{1}{a^n}=a^{-n}\\\\\sqrt[n]{a}=a^{\frac{1}{n}}\\\\a^m\cdot a^n=a^{m+n}[/tex]
