The digit in the unit's place of 13^37 is :

The correct answer is Option (4) → 3

Unit digit of $13^{37}$ = Unit digit of $3^{37}$

$⇒3^{37}=(3^4)^9.3^1$

and,

Unit digit of $3^4=1$

∴ Unit digit of $3^{37}=1.3=3$

⇒ Unit digit of $13^{37}=3$