Explanation

An odd power of 9 always ends in 9, so 9²⁷ ends in 9. Powers of 7 cycle 7, 9, 3, 1 with period 4, and 9 ≡ 1 (mod 4), so 27⁹ (like 7⁹) ends in 7. The last digit of the sum is the last digit of 9 + 7 = 16, i.e. 6 (B).