$a\text{)}{3}^6\cdot {81}^{5}x={27}^4\cdot {\left(9^2\right)}^4$    

$3^6\cdot {\left(3^4\right)}^{5}x={\left(3^3\right)}^4\cdot {\left({\left(3^2\right)}^2\right)}^4$  
$3^6\cdot 3^{20}x=3^{12}\cdot 3^{16}$  
$3^{26}x=3^{28}\mid :3^{26}$  

$x=3^2$  

$x=9$  

$b\text{)}{\left(2^8\right)}^{2}x=2^{17}+2^{15}x$  

$2^{16}x=2^{15}\left(2^2+x\right)\mid :2^{15}$  

$2x=4+x\mid -x$  

$x=4$