a)
If the student has to answer every question without leaving any question blank,
then there are $4$ options and the student can select any one out of these $4$ options in each question
So the number of ways he can answer each question =$4$ ways
$\therefore$ Number of ways to answer $10$ questions$=4*4*4.......(10 $ times$)$
Ans= $4^{10}$ ways
b)
If a student can leave an answer blank,
then the student can either select any one out of the $4$ options or leave it blank for each question
So the number of ways he can answer each question=$5$ ways
$\therefore$ Number of ways to answer $10$ questions$=5*5*5......(10 $ times$)$
Ans=$5^{10}$ ways