$a)2^5-{\left(-2\right)}^5=32-\left(-32\right)=32+32=64$   

$b){\left(\frac{1}{3}\right)}^4+{\left(\frac{-1}{3}\right)}^4=\frac{1}{81}+\frac{1}{81}=\frac{2}{81}$  

$c){\left(\frac{1}{3}\right)}^2\cdot 3^3=\frac{1}{{\sout{9}}_1}\cdot {\sout{27}}^3=3$