a)

$\sqrt{9}\cdot \left[{\left(1,5\right)}^{-1}+9^{-1,5}\right]-{27}^{-\frac{2}{3}}=3\cdot \left[{\left(\frac{3}{2}\right)}^{-1}+{\left(3^2\right)}^{-\frac{3}{2}}\right]-{\left(3^3\right)}^{-\frac{2}{3}}=$     

$=3\cdot \left[\frac{2}{3}+3^{-3}\right]-3^{-2}=3\cdot \left[\frac{2}{3}+\frac{1}{27}\right]-{\left(\frac{1}{3}\right)}^2=3\cdot \left[\frac{18}{27}+\frac{1}{27}\right]-\frac{1}{9}=$  

$={\cancel{3}}^1\cdot \frac{19}{{\cancel{27}}^9}-\frac{1}{9}=\frac{19}{9}-\frac{1}{9}=\frac{18}{9}=2$  

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b)

${\left[{\left(\frac{81}{625}\right)}^{-0,75}:{\left(1\frac{2}{3}\right)}^3-{\left(0,125\right)}^{\frac{1}{3}}\right]}^{-2}={\left[{\left({\left(\frac{3}{5}\right)}^4\right)}^{-\frac{3}{4}}:{\left(\frac{5}{3}\right)}^3-{\left(\frac{1}{8}\right)}^{\frac{1}{3}}\right]}^{-2}=$  

$={\left[{\left(\frac{3}{5}\right)}^{-3}:{\left(\frac{5}{3}\right)}^3-{\left(2^{-3}\right)}^{\frac{1}{3}}\right]}^{-2}={\left[{\left(\frac{5}{3}\right)}^3:{\left(\frac{5}{3}\right)}^3-2^{-1}\right]}^{-2}=$  

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

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c)

$\sqrt[3]{0,375}\cdot \sqrt[3]{9}+{\left(3^{-1}-\sqrt[4]{\frac{16}{81}}\right)}^{-2}=\sqrt[3]{\frac{3}{8}}\cdot \sqrt[3]{9}+{\left(\frac{1}{3}-\sqrt[4]{{\left(\frac{2}{3}\right)}^4}\right)}^{-2}=$  

$=\sqrt[3]{\frac{3}{8}\cdot 9}+{\left(\frac{1}{3}-{\left(\frac{2}{3}\right)}^{\frac{4}{4}}\right)}^{-2}=\sqrt[3]{\frac{27}{8}}+{\left(\frac{1}{3}-\frac{2}{3}\right)}^{-2}=$  

$=\frac{3}{2}+{\left(-\frac{1}{3}\right)}^{-2}=\frac{3}{2}+{\left(-3\right)}^2=\frac{3}{2}+9=10\frac{1}{2}$  

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d)

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

$={\left[\frac{5^2-5}{2^2}\cdot 5^3\right]}^{\frac{3}{4}}={\left[\frac{25-5}{4}\cdot 5^3\right]}^{\frac{3}{4}}={\left[\frac{20}{4}\cdot 5^3\right]}^{\frac{3}{4}}={\left(5\cdot 5^3\right)}^{\frac{3}{4}}=$  

$={\left(5^4\right)}^{\frac{3}{4}}=5^3=125$