$\text{a)}{3}^{-2}\cdot 3^4=3^{-2+4}=3^2=9$     

$\text{b)}{5}^2\cdot 5^{-6}=5^{2+\left(-6\right)}=5^{-4}={\left(\frac{1}{5}\right)}^4=\frac{1}{625}$  

$\text{c)}{4}^{-4}\cdot 4^2=4^{-4+2}=4^{-2}={\left(\frac{1}{4}\right)}^2=\frac{1}{16}$  

$\text{d)}{2}^{-8}\cdot 2^5=2^{-8+5}=2^{-3}={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$  

$\text{e)}{\left(\frac{2}{3}\right)}^{-8}\cdot {\left(\frac{2}{3}\right)}^6={\left(\frac{2}{3}\right)}^{-8+6}={\left(\frac{2}{3}\right)}^{-2}={\left(\frac{3}{2}\right)}^2=\frac{9}{4}=2\frac{1}{4}$  

$\text{f)}{\left(\frac{4}{7}\right)}^{-4}\cdot {\left(\frac{4}{7}\right)}^5={\left(\frac{4}{7}\right)}^{-4+5}={\left(\frac{4}{7}\right)}^1=\frac{4}{7}$  

$\text{g)}{\left(1\frac{2}{3}\right)}^{10}\cdot {\left(1\frac{2}{3}\right)}^{-8}={\left(1\frac{2}{3}\right)}^{10-8}={\left(1\frac{2}{3}\right)}^2={\left(\frac{5}{3}\right)}^2=\frac{25}{9}=2\frac{7}{9}$  

$\text{h)}{\left(2,6\right)}^{-4}\cdot {\left(2,6\right)}^3={\left(2,6\right)}^{-4+3}={\left(2,6\right)}^{-1}={\left(\frac{26}{10}\right)}^{-1}=\frac{10}{26}=\frac{5}{13}$