Ex$\mathrm{.}2($a$",$ but done fast$)$ Suppose you want to calculate the n $^($th$)$ power of a given number a$.$ Suppose you know a $($fix it say to $42),$ but is an input $.$ Perhaps the first thing you would do is to compute a times a times a etc. for n times. How much time would you spend in this case? $($we assume multiplying and addition takes constant time$)$ Can we do better? If yes, how $?$ If not, why not? $($hint: divide and conquer $)$