$a)$

$5^3=5\cdot 5\cdot 5=25\cdot 5=125$

${\left(-4\right)}^4=\left(-4\right)\cdot \left(-4\right)\cdot \left(-4\right)\cdot \left(-4\right)=16\cdot 16=256$

${\left(-3\right)}^5=\left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)\cdot \left(-3\right)=9\cdot 9\cdot \left(-3\right)=81\cdot \left(-3\right)=-243$

${\left(-11\right)}^2=\left(-11\right)\cdot \left(-11\right)=121$