The units’ digit in (53)²¹ + (27)³⁵ − (32)³¹ is equal to:
2019
The units’ digit in (53)²¹ + (27)³⁵ − (32)³¹ is equal to:
- A.
4
- B.
2
- C.
8
- D.
6
Attempted by 138 students.
Show answer & explanation
Correct answer: C
To find the unit digit of the expression (53)^21 + (27)^35 - (32)^31, we focus on the unit digit of each base and its repeating cycle when raised to powers.
Step-by-Step Solution
Analyze each term:
(53)^21: The base is 3. Powers of 3 follow a cycle of 4: {3, 9, 7, 1}.
21 divided by 4 leaves a remainder of 1. The unit digit is the 1st in the cycle, which is 3.
(27)^35: The base is 7. Powers of 7 follow a cycle of 4: {7, 9, 3, 1}.
35 divided by 4 leaves a remainder of 3. The unit digit is the 3rd in the cycle, which is 3.
(32)^31: The base is 2. Powers of 2 follow a cycle of 4: {2, 4, 8, 6}.
31 divided by 4 leaves a remainder of 3. The unit digit is the 3rd in the cycle, which is 8.
Combine the results:
Expression: 3 + 3 - 8
Result: 6 - 8 = -2
When you get a negative result in unit digit problems, add 10 to make it positive: -2 + 10 = 8.