$\text{a)}{2}^8\cdot 2^3=2^{8+3}=2^{11}$  

Odp.:   $x=2^3=8$

 

$\text{b)}{\left(-3\right)}^5:{\left(-3\right)}^0={\left(-3\right)}^{5-0}={\left(-3\right)}^5$   

Odp.:  $x=0$   

 

$\text{c)}{25}^6={\left(5^2\right)}^6=5^{2\cdot 6}=5^{12}$   

${\left(5^6\right)}^2=5^{6\cdot 2}=5^{12}$  

Odp.:  $x=6$

 

$\text{d)}{100}^6={\left({10}^2\right)}^6={10}^{12}$  

${\left({10}^3\right)}^4={10}^{3\cdot 4}={10}^{12}$

Odp.:   $x=4$