The unit digit in (33) ^49 +(52)^ 21 −(27) ^42 is equal to:

Solution: Find the unit digit of each term using repeating cycles of unit digits.

• 33^49 has the same unit digit as 3^49. The cycle for 3 is (3, 9, 7, 1) with period 4. Since 49 mod 4 = 1, the unit digit is 3.

• 52^21 has the same unit digit as 2^21. The cycle for 2 is (2, 4, 8, 6) with period 4. Since 21 mod 4 = 1, the unit digit is 2.

• 27^42 has the same unit digit as 7^42. The cycle for 7 is (7, 9, 3, 1) with period 4. Since 42 mod 4 = 2, the unit digit is 9.

• Combine the unit digits: 3 + 2 − 9 = −4. Convert to a nonnegative unit digit by adding 10: −4 ≡ 6 (mod 10).

Answer: 6