$\text{a)}{\left(-4\right)}^5=\left(-4\right)\cdot \left(-4\right)\cdot \left(-4\right)\cdot \left(-4\right)\cdot \left(-4\right)=-1024$       

$\text{b)}{\left(-5\right)}^4=\left(-5\right)\cdot \left(-5\right)\cdot \left(-5\right)\cdot \left(-5\right)=625$  

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

$\text{d)}{5}^{-3}={\left(\frac{1}{5}\right)}^3=\frac{1}{5}\cdot \frac{1}{5}\cdot \frac{1}{5}=\frac{1}{125}$  

$\text{e)}{\left(1\frac{1}{2}\right)}^6={\left(\frac{3}{2}\right)}^6=\frac{3^6}{2^6}=\frac{9^3}{4^3}=\frac{729}{64}$

$\text{f)}{\left(\frac{13}{7}\right)}^0=1$

$\text{g)}{\left(\frac{5}{9}\right)}^{-1}=\frac{9}{5}$

$\text{h)}{\left(\frac{2}{3}\right)}^{-3}={\left(\frac{3}{2}\right)}^3=\frac{27}{8}$

$\text{i)}{\left(1\frac{1}{4}\right)}^{-3}={\left(\frac{5}{4}\right)}^{-3}={\left(\frac{4}{5}\right)}^3=\frac{64}{125}$

$\text{j)}{\left(3\frac{1}{3}\right)}^{-4}={\left(\frac{10}{3}\right)}^{-4}={\left(\frac{3}{10}\right)}^4=\frac{81}{10000}$