$a)$

$\frac{{\left(-4\right)}^2}{8^2}={\left(-\frac{4}{8}\right)}^2={\left(-\frac{1}{2}\right)}^2=\frac{1}{4}$

$\frac{{\left(0,55\right)}^2}{{\left(0,11\right)}^2}={\left(\frac{0,55}{0,11}\right)}^2=5^2=25$

$\frac{{121}^2}{{11}^2}={\left(\frac{121}{11}\right)}^2={11}^2=121$

$\frac{{196}^2}{{14}^2}={\left(\frac{196}{14}\right)}^2={14}^2=196$  

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$b)$

${\left(-2,5\right)}^3:{\left(0,5\right)}^3=$ ${\left[\left(-2,5\right):0,5\right]}^3$  =  ${\left(-5\right)}^3=-125$

${\left(-1\frac{1}{3}\right)}^4:{\left(\frac{2}{3}\right)}^4={\left[\left(-1\frac{1}{3}\right):\left(\frac{2}{3}\right)\right]}^4={\left[\left(-\frac{4}{3}\right)\cdot \frac{3}{2}\right]}^4={\left(-2\right)}^4=16$  

${\left(-4,8\right)}^6:{\left(-4\frac{4}{5}\right)}^6={\left[\left(-4,8\right):\left(-4\frac{4}{5}\right)\right]}^6={\left[\left(-\frac{48}{10}\right):\left(-\frac{24}{5}\right)\right]}^6={\left[\left(-\frac{24}{5}\right)\cdot \left(-\frac{5}{24}\right)\right]}^6=1^6=1$