$\text{a)}{27}^{\frac{2}{3}}={\left({27}^{\frac{1}{3}}\right)}^2={\left(\sqrt[3]{27}\right)}^2=3^2=9$  

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$\text{b)}{16}^{\frac{3}{4}}={\left({16}^{\frac{1}{4}}\right)}^3={\left(\sqrt[4]{16}\right)}^3=2^3=8$  

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$\text{c)}{49}^{1,5}={49}^{\frac{3}{2}}={\left({49}^{\frac{1}{2}}\right)}^3={\left(\sqrt{49}\right)}^3=7^3=343$  

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$\text{d)}{100}^{2\frac{1}{2}}={100}^{\frac{5}{2}}={\left({100}^{\frac{1}{2}}\right)}^5={\left(\sqrt{100}\right)}^5={10}^5=100000$  

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$\text{e)}{\left(\frac{1}{125}\right)}^{\frac{2}{3}}={\left[{\left(\frac{1}{125}\right)}^{\frac{1}{3}}\right]}^2={\left(\sqrt[3]{\frac{1}{125}}\right)}^2={\left(\frac{1}{5}\right)}^2=\frac{1}{25}$  

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$\text{f)}{0,125}^{-\frac{2}{3}}={\left({0,125}^{\frac{1}{3}}\right)}^{-2}={\left(\sqrt[3]{0,125}\right)}^{-2}={0,5}^{-2}={\left(\frac{1}{2}\right)}^{-2}=2^2=4$  

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$\text{g)}{0,36}^{-1,5}={0,36}^{-\frac{3}{2}}={\left({0,36}^{\frac{1}{2}}\right)}^{-3}={\left(\sqrt{0,36}\right)}^{-3}={0,6}^{-3}={\left(\frac{3}{5}\right)}^{-3}={\left(\frac{5}{3}\right)}^3=\frac{125}{27}$  

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$\text{h)}{0,0001}^{-2,5}={0,0001}^{-\frac{5}{2}}={\left({0,0001}^{\frac{1}{2}}\right)}^{-5}={\left(\sqrt{0,0001}\right)}^{-5}={0,01}^{-5}={\left(\frac{1}{100}\right)}^{-5}={100}^5=10000000000$