Solution

To find the digit in the unit’s place of (1624)²⁴, we only need to consider the units digit of the base, 1624, and then find the pattern in the units digits of its powers. Units digit of 1624: The units digit of 1624 is 4. Find the units digit of 4²⁴:   First, observe the pattern in the units’ digits of the powers of 4:    (4¹ = 4) (units digit = 4)     (4² = 16) (units digit = 6)    (4³ = 64) (units digit = 4)    (4⁴ = 256) (units digit = 6)    The pattern repeats every two powers: 4, 6, 4, 6... Since (24) is even, the units digit of (4²⁴) follows the same pattern:   (4²⁴) corresponds to 4² in the pattern. Unit Digit =6