$\text{a)}3\cdot {\left(-1\right)}^2-2\cdot {\left(-2\right)}^3=3\cdot 1-2\cdot \left(-8\right)=3-\left(-16\right)=3+16=19$

$\text{b)}{\left|-3\right|}^2+2^3-1^6-4^3+1=9+8-1-64+1=-47$

$\text{c)}{\left(-5\right)}^2+2\cdot \left(-5\right)\cdot \left(-4\right)+{\left(-4\right)}^2=25+40+16=81$  

$\text{d)}{\left(-\frac{1}{3}\right)}^2-3\cdot \left|-\frac{1}{3}\right|+6=\frac{1}{9}-1+6=-\frac{8}{9}+6=5\frac{1}{9}$

$\text{e)}\frac{3}{4}\cdot {\left(\frac{2}{3}\right)}^2-\frac{1}{2}\cdot {\left(-4\right)}^3=\frac{3}{{\sout{4}}^1}\cdot \frac{{\sout{4}}^1}{9}-\frac{1}{2}\cdot \left(-64\right)=\frac{1}{3}+32=32\frac{1}{3}$  

$\text{f)}5\cdot {\left(-0,5\right)}^2\cdot {\left(-1\right)}^3+4\cdot \left|-\frac{1}{2}-\left(-1\right)\right|=5\cdot 0,25\cdot \left(-1\right)+4\cdot \left|\frac{1}{2}\right|=-1,25+2=0,75$