5 letter word that can be formed using the letters of the word NATURE begin with N repetition is allowed
consider 5 places 

Fill the first place using N in 1 way Each of the remaining 4 places can be filled using N,A,T,U,R,E in 6 ways 
No. of words =$1\times 6\times 6\times 6\times 6$
                       $=6^4=1296.$
No.of elements in A =n(A)=5
No.of elements in A = n(B) = 4
Total number of functions from A to B =$n(B{)}^{n\left(A\right)}=4^5$