أولاً نبسّط الأساس: (77+3) = 80. Reduce it modulo 7: 80 ≡ 3 (mod 7). The powers of 3 modulo 7 repeat in the cycle 3, 2, 6, 4, 5, 1. Since exponent 82 points to the cycle value 4, 80^82 leaves remainder 4.