What is the unit digit in the product (3⁶⁵ × 6⁵⁹ × 7⁷¹)?

Solution (By Examveda Team)

Unit digit in 3⁴ = 1 ⇒ Unit digit in (3⁴)¹⁶ = 1
Therefore Unit digit in 3⁶⁵ = Unit digit in [ (3⁴)¹⁶ × 3 ] = (1 × 3) = 3
Unit digit in 6⁵⁹ = 6
Unit digit in 7⁴ ⇒ Unit digit in (7⁴)¹⁷ is 1
Unit digit in 7⁷¹ = Unit digit in [(7⁴)¹⁷ × 7³] = (1 × 3) = 3
Therefore Required digit = Unit digit in (3 × 6 × 3) = 4