$\text{a)}{\left(\frac{1}{4}\right)}^4=\frac{1}{4}\cdot \frac{1}{4}\cdot \frac{1}{4}\cdot \frac{1}{4}=\frac{1}{256}$

$\text{b)}{\left(\frac{2}{3}\right)}^4=\frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}\cdot \frac{2}{3}=\frac{4}{9}\cdot \frac{4}{9}=\frac{16}{81}$

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

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

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

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

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

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