$a)5^3=5\cdot 5\cdot 5=25\cdot 5=125$  

$2^5=2\cdot 2\cdot 2\cdot 2\cdot 2=4\cdot 4\cdot 2=16\cdot 2=32$  

${\left(-3\right)}^4=\left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)=9\cdot 9=81$  

${\left(-4\right)}^3=\left(-4\right)\cdot \left(-4\right)\cdot \left(-4\right)=16\cdot \left(-4\right)=-64$  

$b)0^6=0$  

${\left(1\frac{3}{7}\right)}^1=1\frac{3}{7}$  

${\left(-1\right)}^4=\left(-1\right)\cdot \left(-1\right)\cdot \left(-1\right)\cdot \left(-1\right)=1\cdot 1=1$  

${\left(-10\right)}^0=1$  

$c){\left(\frac{1}{2}\right)}^5=\frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}\cdot \frac{1}{4}\cdot \frac{1}{2}=\frac{1}{16}\cdot \frac{1}{2}=\frac{1}{32}$  

${\left(-\frac{3}{5}\right)}^4=\left(-\frac{3}{5}\right)\cdot \left(-\frac{3}{5}\right)\cdot \left(-\frac{3}{5}\right)\cdot \left(-\frac{3}{5}\right)=\frac{9}{25}\cdot \frac{9}{25}=\frac{81}{625}$

${0,2}^6=0,2\cdot 0,2\cdot 0,2\cdot 0,2\cdot 0,2\cdot 0,2=0,04\cdot 0,04\cdot 0,04=0,0016\cdot 0,04=0,000064$

${\left(-0,03\right)}^3=\left(-0,03\right)\cdot \left(-0,03\right)\cdot \left(-0,03\right)=0,0009\cdot \left(-0,03\right)=-0,000027$

$d){\left(-1,1\right)}^2=\left(-1,1\right)\cdot \left(-1,1\right)=1,21$  

${\left(1\frac{1}{4}\right)}^3={\left(\frac{5}{4}\right)}^3=\frac{5}{4}\cdot \frac{5}{4}\cdot \frac{5}{4}=\frac{125}{64}=1\frac{61}{64}$

${\left(-2\frac{1}{5}\right)}^3={\left(-\frac{11}{5}\right)}^3=\left(-\frac{11}{5}\right)\cdot \left(-\frac{11}{5}\right)\cdot \left(-\frac{11}{5}\right)=\frac{121}{25}\cdot \left(-\frac{11}{5}\right)=-\frac{1331}{125}$

${1,3}^2=1,3\cdot 1,3=1,69$  

$e)-3^4=-\left(3\cdot 3\cdot 3\cdot 3\right)=-\left(9\cdot 9\right)=-81$  

$-{\left(-1,5\right)}^3=-{\left(-\frac{15}{10}\right)}^3=-{\left(-\frac{3}{2}\right)}^3=-\left(\left(-\frac{3}{2}\right)\cdot \left(-\frac{3}{2}\right)\cdot \left(-\frac{3}{2}\right)\right)=-\left(\frac{9}{4}\cdot \left(-\frac{3}{2}\right)\right)=-\left(-\frac{27}{8}\right)=\frac{27}{8}=3\frac{3}{8}$   $-{1,1}^2=-\left(1,1\cdot 1,1\right)=-1,21$  

$-{\left(-\frac{2}{3}\right)}^4=$   $-\left(-\frac{2}{3}\cdot \left(-\frac{2}{3}\right)\cdot \left(-\frac{2}{3}\right)\cdot \left(-\frac{2}{3}\right)\right)$ = $-\left(\frac{4}{9}\cdot \frac{4}{9}\right)=$   $-\frac{16}{81}$  

$f)\frac{2^3}{3}=\frac{2\cdot 2\cdot 2}{3}=\frac{8}{3}=2\frac{2}{3}$

$\frac{{\left(-3\right)}^2}{2}=\frac{-3\cdot \left(-3\right)}{2}=\frac{9}{2}=4\frac{1}{2}$   

$\frac{2}{3^2}=\frac{2}{3\cdot 3}=\frac{2}{9}$  

$\frac{-5^3}{{\left(-3\right)}^2}=\frac{-\left(5\cdot 5\cdot 5\right)}{\left(-3\right)\cdot \left(-3\right)}=-\frac{125}{9}=-13\frac{8}{9}$