$\text{a)}{2}^3=2\cdot 2\cdot 2=8$

$\text{b)}{6}^2=6\cdot 6=36$

$\text{c)}{\left(-4\right)}^2=\left(-4\right)\cdot \left(-4\right)=16$

$\text{d)}{\left(-2\right)}^3=\left(-2\right)\cdot \left(-2\right)\cdot \left(-2\right)=-8$

$\text{e)}{\left(\frac{1}{3}\right)}^3=\frac{1}{3}\cdot \frac{1}{3}\cdot \frac{1}{3}=\frac{1}{27}$

$\text{f)}{\left(\frac{2}{5}\right)}^4=\frac{2}{5}\cdot \frac{2}{5}\cdot \frac{2}{5}\cdot \frac{2}{5}=\frac{16}{625}$

$\text{g)}{\left(\frac{5}{4}\right)}^2=\frac{5}{4}\cdot \frac{5}{4}=\frac{25}{16}=1\frac{9}{16}$

$\text{h)}{\left(-\frac{3}{7}\right)}^2=\left(-\frac{3}{7}\right)\cdot \left(-\frac{3}{7}\right)=\frac{9}{49}$

$\text{i)}{\left(-\frac{2}{10}\right)}^3=\left(-\frac{2}{10}\right)\cdot \left(-\frac{2}{10}\right)\cdot \left(-\frac{2}{10}\right)=\frac{4}{100}\cdot \left(-\frac{2}{10}\right)=-\frac{8}{1000}=-\frac{1}{125}$