$\text{a)}{3}^5\cdot 3^2:3^{-1}=3^{5+2}:3^{-1}=3^{7-\left(-1\right)}=3^8$      

$\text{b)}{\left(\sqrt{7}\right)}^3\cdot {\left(\sqrt{7}\right)}^{-3}\cdot {\left(\sqrt{7}\right)}^0={\left(\sqrt{7}\right)}^{3-3+0}={\left(\sqrt{7}\right)}^0$

$\text{c)}\left(0,5\right)\cdot {\left(0,5\right)}^{-7}={\left(0,5\right)}^{1+\left(-7\right)}={\left(0,5\right)}^{-6}$  

$\text{d)}{\left(-4\right)}^{-10}\cdot {\left(-4\right)}^{-7}={\left(-4\right)}^{-10+\left(-7\right)}={\left(-4\right)}^{-17}$  

$\text{e)}{\left(0,3\right)}^{-2}\cdot {\left(0,3\right)}^3={\left(0,3\right)}^{-2+3}={\left(0,3\right)}^1$  

$\text{f)}{\left(-3\frac{3}{4}\right)}^5:{\left(-3\frac{3}{4}\right)}^{-5}={\left(-3\frac{3}{4}\right)}^{5-\left(-5\right)}={\left(-3\frac{3}{4}\right)}^{10}$  

$\text{g)}\left(-1\right):{\left(-1\right)}^9:{\left(-1\right)}^6={\left(-1\right)}^{1-9}:{\left(-1\right)}^6={\left(-1\right)}^{-8}:{\left(-1\right)}^6={\left(-1\right)}^{-8-6}={\left(-1\right)}^{-14}$  

$\text{h)}{\left(\frac{1}{2}\right)}^{-5}:{\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^{-5-3}={\left(\frac{1}{2}\right)}^{-8}$