$a\text{)}{169}^{\frac{1}{2}}=\sqrt{169}=13$  

$b\text{)}{27}^{\frac{1}{3}}=\sqrt[3]{27}=3$  

$c\text{)}{256}^{\frac{1}{4}}=\sqrt[4]{256}=4$  

$d\text{)}{125}^{\frac{2}{3}}={\left(\sqrt[3]{125}\right)}^2=5^2=25$  

$e\text{)}{16}^{\frac{3}{4}}={\left(\sqrt[4]{16}\right)}^3=2^3=8$  

$f\text{)}{8}^{-\frac{2}{3}}={\left(\frac{1}{8}\right)}^{\frac{2}{3}}={\left(\frac{\sqrt[3]{1}}{8}\right)}^2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$  

$g\text{)}{\left(2\frac{1}{4}\right)}^{-\frac{1}{2}}={\left(\frac{9}{4}\right)}^{-\frac{1}{2}}={\left(\frac{4}{9}\right)}^{\frac{1}{2}}=\sqrt{\frac{4}{9}}=\frac{2}{3}$