$b)$  

$p=2^{\pi -1}\cdot 2^{\frac{1}{2}-\pi }=2^{\pi -1+\frac{1}{2}-\pi }=2^{-\frac{1}{2}}$ $p=2^{\pi -1}\cdot 2^{\frac{1}{2}-\pi }=2^{\pi -1+\frac{1}{2}-\pi }=2^{-\frac{1}{2}}$  

 

 

$c)$  

$p=2^{\sqrt{2}+3}:2^{\sqrt{2}-\frac{1}{4}}=2^{\sqrt{2}+3-\left(\sqrt{2}-\frac{1}{4}\right)}=2^{\sqrt{2}+3-\sqrt{2}+\frac{1}{4}}=2^{3\frac{1}{4}}=2^{\frac{13}{4}}$  

 

 

$d)$    

$p=2^{\sqrt{3}+5}:2^{\sqrt{5}+5}=2^{\sqrt{3}+5-\left(\sqrt{5}+5\right)}=2^{\sqrt{3}+5-\sqrt{5}-5}=2^{\sqrt{3}-\sqrt{5}}$