$\text{a)}{4}^{-3}={\left(\frac{1}{4}\right)}^3=\frac{1}{64}$  

$\text{b)}{3}^{-4}={\left(\frac{1}{3}\right)}^4=\frac{1}{81}$  

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

$\text{d)}{\left(\frac{3}{4}\right)}^{-2}={\left(\frac{4}{3}\right)}^2=\frac{16}{9}=1\frac{7}{9}$  

$\text{e)}\frac{2^3\cdot 2^4}{2^5}=\frac{2^7}{2^5}=2^2=4$   

$\text{f)}\frac{5^4\cdot 5^{-2}}{5^3}=\frac{5^2}{5^3}=5^{-1}=\frac{1}{5}$  

$\text{g)}\frac{3^6\cdot 9}{3^5}=\frac{3^6\cdot 3^2}{3^5}=\frac{3^8}{3^5}=3^3=27$  

$\text{h)}\frac{6^4\cdot {36}^{-1}}{6^{-1}}=\frac{6^4\cdot {\left(6^2\right)}^{-1}}{6^{-1}}=\frac{6^4\cdot 6^{-2}}{6^{-1}}=\frac{6^2}{6^{-1}}=6^3=216$