$a)$

$4^5:4^3=4^{5-3}=4^2=16$  
 
${\left(-2\right)}^7:{\left(-2\right)}^1={\left(-2\right)}^{7-1}={\left(-2\right)}^6=64$

${\left(-3\right)}^0:{\left(-3\right)}^0={\left(-3\right)}^{0-0}={\left(-3\right)}^0=1$

---

$b)$

${\left(\frac{1}{4}\right)}^3:\frac{1}{4}={\left(\frac{1}{4}\right)}^{3-1}={\left(\frac{1}{4}\right)}^2=\frac{1}{16}$

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

${\left(-1,5\right)}^3:{\left(-1,5\right)}^0={\left(-1,5\right)}^{3-0}={\left(-1,5\right)}^3=-3,375$