$\text{a)}\sqrt{3}=3^{\frac{1}{2}}$   

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$\text{b)}\sqrt[3]{{15}^2}={\left({15}^2\right)}^{\frac{1}{3}}={15}^{2\cdot \frac{1}{3}}={15}^{\frac{2}{3}}$  

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$\text{c)}\sqrt[5]{2}=2^{\frac{1}{5}}$  

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$\text{d)}\sqrt[3]{-5}={\left(-5\right)}^{\frac{1}{3}}$  

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$\text{e)}\sqrt[8]{7^{-5}}={\left(7^{-5}\right)}^{\frac{1}{8}}=7^{-5\cdot \frac{1}{8}}=7^{-\frac{5}{8}}$  

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$\text{f)}\sqrt[10]{{0,1}^3}={\left({0,1}^3\right)}^{\frac{1}{10}}={0,1}^{3\cdot \frac{1}{10}}={0,1}^{\frac{3}{10}}$