$\text{a)}\sqrt{7}=7^{\frac{1}{2}}$  

$\text{b)}\sqrt[3]{37}={37}^{\frac{1}{3}}$      

$\text{c)}\sqrt[4]{0,4}={\left(0,4\right)}^{\frac{1}{4}}={\left(\frac{4}{10}\right)}^{\frac{1}{4}}={\left(\frac{2}{5}\right)}^{\frac{1}{4}}$  

$\text{d)}\sqrt{\frac{1}{5}}={\left(\frac{1}{5}\right)}^{\frac{1}{2}}$  

$\text{e)}\sqrt[5]{1\frac{1}{10}}={\left(1\frac{1}{10}\right)}^{\frac{1}{5}}={\left(\frac{11}{10}\right)}^{\frac{1}{5}}$  

$\text{f)}\frac{1}{\sqrt{3}}=\frac{1}{3^{\frac{1}{2}}}={\left(\frac{1}{3}\right)}^{\frac{1}{2}}=3^{-\frac{1}{2}}$  

$\text{g)}\frac{1}{\sqrt{0,1}}=\frac{1}{{\left(0,1\right)}^{\frac{1}{2}}}={\left(\frac{1}{0,1}\right)}^{\frac{1}{2}}={10}^{\frac{1}{2}}$  

$\text{h)}\frac{1}{\sqrt[3]{7}}=\frac{1}{7^{\frac{1}{3}}}={\left(\frac{1}{7}\right)}^{\frac{1}{3}}=7^{-\frac{1}{3}}$  

$\text{i)}\frac{1}{\sqrt[4]{3,9}}=\frac{1}{{\left(3,9\right)}^{\frac{1}{4}}}={\left(\frac{1}{3,9}\right)}^{\frac{1}{4}}={\left(\frac{10}{39}\right)}^{\frac{1}{4}}$  

$\text{j)}\frac{1}{\sqrt[10]{0,09}}=\frac{1}{{\left(0,09\right)}^{\frac{1}{10}}}={\left(\frac{1}{0,09}\right)}^{\frac{1}{10}}={\left(\frac{100}{9}\right)}^{\frac{1}{10}}$