$a){\left(0,25\right)}^x=2^8$  

${\left(\frac{1}{4}\right)}^x=2^8$  

${\left(4^{-1}\right)}^x=2^8$  

$4^{-x}=2^8$  

${\left(2^2\right)}^{-x}=2^8$  

$2^{-2x}=2^8$  

$-2x=8\mid :\left(-2\right)$  

$x=-4$  

$b)2^x={\left(0,5\right)}^6$  

$2^x={\left(\frac{1}{2}\right)}^6$  

$2^x=2^{-6}$  

$x=-6$  

$c){\left(0,2\right)}^x={25}^3$  

${\left(\frac{1}{5}\right)}^x={\left(5^2\right)}^3$  

${\left(5^{-1}\right)}^x=5^6$  

$5^{-x}=5^6$  

$-x=6\mid \cdot \left(-1\right)$  

$x=-6$  

$d){\left(2^3\right)}^x={\left(0,125\right)}^3$  

$2^{3x}={\left(\frac{1}{8}\right)}^3$  

$2^{3x}={\left({\left(\frac{1}{2}\right)}^3\right)}^3$  

$2^{3x}={\left(\frac{1}{2}\right)}^9$  

$3x=9\mid :3$  

$x=3$