$\text{a)}$  

${49}^{\frac{1}{2}}=\sqrt{49}=7$  

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$8^{\frac{1}{3}}=\sqrt[3]{8}=2$  

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${0,0016}^{\frac{1}{4}}=\sqrt[4]{0,0016}=0,2$  

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${\left(\frac{1}{128}\right)}^{\frac{1}{7}}=\sqrt[7]{\frac{1}{128}}=\frac{1}{2}$  

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${0,00001}^{\frac{1}{5}}=\sqrt[5]{0,00001}=0,1$  

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$\text{b)}$  

${64}^{\frac{4}{3}}={\left(\sqrt[3]{64}\right)}^4=4^4=256$  

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${81}^{\frac{3}{4}}={\left(\sqrt[4]{81}\right)}^3=3^3=27$  

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${243}^{0,2}={243}^{\frac{1}{5}}=\sqrt[5]{243}=3$  

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${32}^{0,8}={32}^{\frac{4}{5}}={\left(\sqrt[5]{32}\right)}^4=2^4=16$  

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${0,25}^{1,5}={\left(0,25\right)}^{\frac{3}{2}}={\left(\sqrt{0,25}\right)}^3={0,5}^3=0,125$  

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$\text{c)}$  

$4^{\frac{-1}{2}}={\left(\frac{1}{4}\right)}^{\frac{1}{2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$  

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${0,125}^{\frac{-2}{3}}={\left(\frac{1}{8}\right)}^{\frac{-2}{3}}=8^{\frac{2}{3}}={\left(\sqrt[3]{8}\right)}^2=2^2=4$  

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${0,36}^{-\frac{3}{2}}={\left(\frac{36}{100}\right)}^{-\frac{3}{2}}={\left(\frac{9}{25}\right)}^{-\frac{3}{2}}={\left(\frac{25}{9}\right)}^{\frac{3}{2}}={\left(\sqrt{\frac{25}{9}}\right)}^3={\left(\frac{5}{3}\right)}^3=\frac{125}{27}=4\frac{17}{27}$   

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${625}^{-0,75}={625}^{-\frac{3}{4}}={\left(\frac{1}{625}\right)}^{\frac{3}{4}}={\left(\sqrt[4]{\frac{1}{625}}\right)}^3={\left(\frac{1}{5}\right)}^3=\frac{1}{125}$  

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${0,16}^{-2,5}={\left(\frac{16}{100}\right)}^{-\frac{5}{2}}={\left(\frac{4}{25}\right)}^{-\frac{5}{2}}={\left(\frac{25}{4}\right)}^{\frac{5}{2}}={\left(\sqrt{\frac{25}{4}}\right)}^5={\left(\frac{5}{2}\right)}^5=\frac{3125}{32}=97\frac{21}{32}$