$\text{a)}$

$4^2=16$

${\left(-3\right)}^3=-3^3=-27$

$7^0=1$  

$1^5=1$  

${\left(-1\right)}^{10}=1^{10}=1$  

$-1^9=-1$

$-2^3=-8$

$-3^0=-1$  

$\text{b)}$

$-{0,1}^2=-0,01$  

${\left(0,3\right)}^2=0,09$  

${\left(-\frac{1}{3}\right)}^3=-\frac{1}{27}$  

${\left(-1\frac{1}{2}\right)}^4={\left(\frac{3}{2}\right)}^4=\frac{81}{16}=5\frac{1}{16}$  

${\left(-\frac{2}{5}\right)}^2={\left(\frac{2}{5}\right)}^2=\frac{4}{25}$  

$-{0,4}^2=-0,016$  

${\left(-0,2\right)}^5={\left(-0,1\cdot 2\right)}^5={\left(-0,1\right)}^5\cdot 2^5=-0,00001\cdot 32=-0,00032$

$\text{c)}$  

${\left(\sqrt{3}\right)}^2=3$  

${\left(-\sqrt[3]{5}\right)}^3=-5$  

${\left(\sqrt[3]{-2}\right)}^3=-2$  

${\left(\sqrt{2}\right)}^4=2^2=4$  

${\left(\sqrt[3]{-3}\right)}^6=$ ${\left({\left(\sqrt[3]{-3}\right)}^3\right)}^2={\left(-3\right)}^2=9$

${\left(2\sqrt{3}\right)}^2=2^2\cdot {\left(\sqrt{3}\right)}^2=4\cdot 3=12$  

${\left(3\sqrt[3]{5}\right)}^3=3^3\cdot {\left(\sqrt[3]{5}\right)}^3=27\cdot 5=135$