$\text{a)}{2}^{1\frac{3}{4}}=2^{\frac{7}{4}}=\sqrt[4]{2^7}$  

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$\text{b)}{2}^{-2,4}=2^{-2\frac{2}{5}}=2^{-\frac{12}{5}}=\sqrt[5]{2^{-12}}$  

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$\text{c)}{0,25}^{0,6}={\left(\frac{1}{4}\right)}^{\frac{3}{5}}={\left[{\left(\frac{1}{2}\right)}^2\right]}^{\frac{3}{5}}={\left(2^{-2}\right)}^{\frac{3}{5}}=2^{-\frac{6}{5}}=\sqrt[5]{2^{-6}}$  

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$\text{d)}{0,0625}^{\frac{5}{6}}={\left(\frac{1}{16}\right)}^{\frac{5}{6}}={\left[{\left(\frac{1}{2}\right)}^4\right]}^{\frac{5}{6}}={\left(2^{-4}\right)}^{\frac{5}{6}}=2^{-\frac{20}{6}}=2^{-\frac{10}{3}}=\sqrt[3]{2^{-10}}$