Question

What is the digiy in units place of143^66×1354^22222?

Answer 1

unit digit in 143^66 will be same as unit digit in 3^66
unit digit in
3^1=3
3^2 =9
3^3=7
3^4=1
3^5 now again 3
this repeats after power 4
so we see that on dividing 66 by 4 remainder is 2
thus last digit in 3^66 = 9
therefore unit digit in 143^66 =9
now same as unit digit in 1354^22222 will be same as in 4^22222
unit digit in
4^1 = 4
4^2=6
4^3=4 here it repeats now we can see that for odd power we get 4 and for even power we get 6
thus unit digit in 4^22222 = 6
now for unit digit in whole expression
multiply 9*6 = 54
unit digit in 54 = 4
thus unit digit will be 4