$\text{a)}{2}^6=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=64$  

$\text{b)}{3}^5=3\cdot 3\cdot 3\cdot 3\cdot 3=243$  

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

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

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

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

$\text{g)}{\left(-6\right)}^{-3}={\left(-\frac{1}{6}\right)}^3=\left(-\frac{1}{6}\right)\cdot \left(-\frac{1}{6}\right)\cdot \left(-\frac{1}{6}\right)=-\frac{1}{216}$  

$\text{h)}{\left(-9\right)}^{-3}={\left(-\frac{1}{9}\right)}^3=\left(-\frac{1}{9}\right)\cdot \left(-\frac{1}{9}\right)\cdot \left(-\frac{1}{9}\right)=-\frac{1}{729}$