a)

${16}^{\frac{1}{3}}\cdot {16}^{\frac{1}{6}}={16}^{\left(\frac{1}{3}+\frac{1}{6}\right)}={16}^{\left(\frac{2}{6}+\frac{1}{6}\right)}={16}^{\frac{3}{6}}={16}^{\frac{1}{2}}=\sqrt{16}=4$

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b) 

${\left(\frac{3}{20}\right)}^{\frac{1}{4}}\cdot {\left(\frac{5}{12}\right)}^{\frac{1}{4}}={\left(\frac{3}{20}\cdot \frac{5}{12}\right)}^{\frac{1}{4}}={\left(\frac{15}{240}\right)}^{\frac{1}{4}}={\left(\frac{1}{16}\right)}^{\frac{1}{4}}=\sqrt[4]{\frac{1}{16}}=\frac{1}{2}$   

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c)

$3^{\frac{3}{2}}:\sqrt{3}=3^{\frac{3}{2}}:3^{\frac{1}{2}}=3^1=3$  

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d)

$\left(25\sqrt{5}\right):5^{\frac{3}{2}}=5^2\cdot 5^{\frac{1}{2}}:5^{\frac{3}{2}}=5^{\frac{5}{2}}:5^{\frac{3}{2}}=5^1=5$  

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e)

${15}^{0,5}\cdot {0,36}^{0,25}={15}^{\frac{1}{2}}\cdot {\left({0,6}^2\right)}^{\frac{1}{4}}={15}^{\frac{1}{2}}\cdot {\left(0,6\right)}^{\frac{1}{2}}={\left(15\cdot 0,6\right)}^{\frac{1}{2}}=9^{\frac{1}{2}}=\sqrt{9}=3$  

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f)

${20}^{\frac{1}{3}}\cdot {\left(2,5\right)}^{-\frac{1}{3}}={20}^{\frac{1}{3}}\cdot {\left(\frac{5}{2}\right)}^{-\frac{1}{3}}={20}^{\frac{1}{3}}\cdot {\left(\frac{2}{5}\right)}^{\frac{1}{3}}={\left(20\cdot \frac{2}{5}\right)}^{\frac{1}{3}}=8^{\frac{1}{3}}=\sqrt[3]{8}=2$  

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g)

$\left(6^{\frac{2}{3}}\cdot 6^{\frac{3}{2}}\right):6^{\frac{1}{6}}=6^{\left(\frac{2}{3}+\frac{3}{2}\right)}:6^{\frac{1}{6}}=6^{\left(\frac{4}{6}+\frac{9}{6}\right)}:6^{\frac{1}{6}}=6^{\frac{13}{6}}:6^{\frac{1}{6}}=6^{\frac{12}{6}}=6^2=36$  

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h)

$7:\left(7^{\frac{1}{3}}\cdot \sqrt{7}\right)=7:\left(7^{\frac{1}{3}}\cdot 7^{\frac{1}{2}}\right)=7:7^{\left(\frac{1}{3}\right)+\left(\frac{1}{2}\right)}=7:7^{\left(\frac{2}{6}\right)+\left(\frac{3}{6}\right)}=7:7^{\frac{5}{6}}=7^{\frac{1}{6}}=\sqrt[6]{7}$