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

$b)4^{-4}\cdot 4^5=4^{-4+5}=4^1$  

$c){\left(\frac{3}{5}\right)}^{-3}\cdot {\left(\frac{3}{5}\right)}^{-2}={\left(\frac{3}{5}\right)}^{-3+\left(-2\right)}={\left(\frac{3}{5}\right)}^{-5}$ $c){\left(\frac{3}{5}\right)}^{-3}\cdot {\left(\frac{3}{5}\right)}^{-2}={\left(\frac{3}{5}\right)}^{-3+\left(-2\right)}={\left(\frac{3}{5}\right)}^{-5}$  

$d){0,36}^3\cdot {0,36}^{-7}={0,36}^{3+\left(-7\right)}={0,36}^{-4}$  

$e){\left(\frac{2}{7}\right)}^{-3}\cdot {\left(\frac{2}{7}\right)}^{-2}={\left(\frac{2}{7}\right)}^{-3+\left(-2\right)}={\left(\frac{2}{7}\right)}^{-5}$  

$f){56}^{45}\cdot {56}^{-55}={56}^{45+\left(-55\right)}={56}^{-10}$  

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

$h)4^{-4}:4^5=4^{-4-5}=4^{-9}$  

$i){\left(\frac{3}{5}\right)}^{-3}:{\left(\frac{3}{5}\right)}^{-2}={\left(\frac{3}{5}\right)}^{-3-\left(-2\right)}={\left(\frac{3}{5}\right)}^{-3+2}={\left(\frac{3}{5}\right)}^{-1}$  

$j){0,36}^3:{0,36}^{-7}={0,36}^{3-\left(-7\right)}={0,36}^{3+7}={0,36}^{10}$  

$k){\left(\frac{2}{7}\right)}^{-3}:{\left(\frac{2}{7}\right)}^{-2}={\left(\frac{2}{7}\right)}^{-3-\left(-2\right)}={\left(\frac{2}{7}\right)}^{-3+2}={\left(\frac{2}{7}\right)}^{-1}$  

$l){56}^{45}:{56}^{-55}={56}^{45-\left(-55\right)}={56}^{45+55}={56}^{100}$