$\text{a)}{\left(\frac{3}{4}\right)}^5\cdot {\left(1\frac{1}{3}\right)}^4={\left(\frac{3}{4}\right)}^5\cdot {\left(\frac{4}{3}\right)}^4=\frac{3}{4}\cdot {\left(\frac{3}{4}\right)}^4\cdot {\left(\frac{4}{3}\right)}^4=\frac{3}{4}\cdot {\left(\frac{{\sout{3}}^1}{{\sout{4}}^1}\cdot \frac{{\sout{4}}^1}{{\sout{3}}^1}\right)}^4=\frac{3}{4}\cdot 1^4=\frac{3}{4}$   

$\text{b)}{0,6}^9\cdot {\left(1\frac{2}{3}\right)}^{11}={\left(\frac{3}{5}\right)}^9\cdot {\left(\frac{5}{3}\right)}^{11}={\left(\frac{3}{5}\right)}^9\cdot {\left(\frac{5}{3}\right)}^9\cdot {\left(\frac{5}{3}\right)}^2={\left(\frac{{\sout{3}}^1}{{\sout{5}}^1}\cdot \frac{{\sout{5}}^1}{{\sout{3}}^1}\right)}^9\cdot {\left(\frac{5}{3}\right)}^2=1^9\cdot \frac{25}{9}=\frac{25}{9}$ $\text{b)}{0,6}^9\cdot {\left(1\frac{2}{3}\right)}^{11}={\left(\frac{3}{5}\right)}^9\cdot {\left(\frac{5}{3}\right)}^{11}={\left(\frac{3}{5}\right)}^9\cdot {\left(\frac{5}{3}\right)}^9\cdot {\left(\frac{5}{3}\right)}^2={\left(\frac{{\sout{3}}^1}{{\sout{5}}^1}\cdot \frac{{\sout{5}}^1}{{\sout{3}}^1}\right)}^9\cdot {\left(\frac{5}{3}\right)}^2=1^9\cdot \frac{25}{9}=\frac{25}{9}$   

$\text{c)}{\left(2,25\right)}^7\cdot {\left(\frac{2}{3}\right)}^{15}={\left(2\frac{1}{4}\right)}^7\cdot {\left(\frac{2}{3}\right)}^{15}={\left(\frac{9}{4}\right)}^7\cdot {\left(\frac{2}{3}\right)}^{15}={\left({\left(\frac{3}{2}\right)}^2\right)}^7\cdot {\left(\frac{2}{3}\right)}^{15}={\left(\frac{3}{2}\right)}^{14}\cdot {\left(\frac{2}{3}\right)}^{14}\cdot \frac{2}{3}=$     

$={\left(\frac{{\sout{3}}^1}{{\sout{2}}^1}\cdot \frac{{\sout{2}}^1}{{\sout{3}}^1}\right)}^{14}\cdot \frac{2}{3}=1^{14}\cdot \frac{2}{3}=\frac{2}{3}$   

$\text{d)}{\left(\frac{1}{3}\right)}^6\cdot 6^5=\frac{1}{3}\cdot {\left(\frac{1}{3}\right)}^5\cdot 6^5=\frac{1}{3}\cdot {\left(\frac{6}{3}\right)}^5=\frac{1}{3}\cdot 2^5=\frac{1}{3}\cdot 32=\frac{32}{3}$  

$\text{e)}{4}^5\cdot {\left(\frac{3}{8}\right)}^4=4\cdot 4^4\cdot {\left(\frac{3}{8}\right)}^4=4\cdot {\left({\sout{4}}^1\cdot \frac{3}{{\sout{8}}^2}\right)}^4=4\cdot {\left(\frac{3}{2}\right)}^4={\sout{4}}^1\cdot \frac{81}{{\sout{16}}^4}=\frac{81}{4}$    

$\text{f)}{\left(3,75\right)}^3\cdot {\left(\frac{4}{5}\right)}^4={\left(3\frac{3}{4}\right)}^3\cdot {\left(\frac{4}{5}\right)}^4={\left(\frac{15}{4}\right)}^3\cdot {\left(\frac{4}{5}\right)}^3\cdot \frac{4}{5}={\left(\frac{{\sout{15}}^3}{{\sout{4}}^1}\cdot \frac{{\sout{4}}^1}{{\sout{5}}^1}\right)}^3\cdot \frac{4}{5}=3^3\cdot \frac{4}{5}=27\cdot \frac{4}{5}=\frac{108}{5}$