What is the last digit of the sum S=9^{27}+27^{9}?

Explanation

The unit digit of 9^{27} is 9 (since 9 raised to any odd power ends in 9). The unit digit of 27^9 relies on 7^9. The cycle of powers of 7 is (7, 9, 3, 1). Since 9 \equiv 1 \pmod 4, it ends in 7. Summing the last digits gives 9 + 7 = 16. The final digit is 6.

Related questions on Arithmetic

• What is the remainder when (17^{25} + 19^{25}) is divided by 18?
• A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what rat...
• Let P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the numbe...
• Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X an...
• Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number...