a) 

$3^0=1$  

$3^1=3$  

$3^2=3\cdot 3=9$  

$3^3=3\cdot 3\cdot 3=27$  

$3^4=3\cdot 3\cdot 3\cdot 3=9\cdot 9=81$  

$3^5=3\cdot 3\cdot 3\cdot 3\cdot 3=9\cdot 9\cdot 3=81\cdot 3=243$  

b) 

${\left(\frac{2}{3}\right)}^0=1$  

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

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

${\left(\frac{2}{3}\right)}^3=\frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}=\frac{4}{9}\cdot \frac{2}{3}=\frac{8}{27}$  

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

${\left(\frac{2}{3}\right)}^5=\frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}=\frac{4}{9}\cdot \frac{4}{9}\cdot$ $\frac{2}{3}=\frac{16}{81}\cdot \frac{2}{3}=\frac{32}{243}$