$a)8^x\cdot {\left(\frac{1}{4}\right)}^x={\left({\sout{8}}^2\cdot \frac{1}{{\sout{4}}^1}\right)}^x=2^x$  

$b){14}^{-x}\cdot {0,1}^{-x}={\left(14\cdot 0,1\right)}^{-x}={1,4}^{-x}$  

$c){16}^x:{\left(\frac{1}{2}\right)}^x={\left(16:\frac{1}{2}\right)}^x={\left(16\cdot 2\right)}^x={32}^x$  

$d)7^x\cdot {\left(\frac{1}{14}\right)}^x\cdot {16}^x={\left({\sout{7}}^1\cdot \frac{1}{{\sout{14}}^2}\cdot 16\right)}^x={\left(\frac{16}{2}\right)}^x=8^x$  

$e){\left(\frac{3}{4}\right)}^{-x}:{\left(\frac{5}{4}\right)}^{-x}={\left(\frac{3}{4}:\frac{5}{4}\right)}^{-x}={\left(\frac{3}{{\sout{4}}^1}\cdot \frac{{\sout{4}}^1}{5}\right)}^{-x}={\left(\frac{3}{5}\right)}^{-x}$