Let a be a positive integer. Let n # a equal n²ª if a is odd and n³ª if a is even. Then (2 # 3) + (3 # 2) – (3 # 3) is equal to A. 64 B. 82 C. 128 D. 512 E. 1522
(A) Let's calculate expressions within brackets first.
(2 # 3) corresponds to (n # a), where n = 2, a = 3. Since 3 is odd, then the we use formula n²ª to calculate the result. It equals 2 to the (2 × 3)th power, which can be calculated as (2³)² = 8² = 64.
(3 # 2) corresponds to (n # a), where n = 3, a = 2. Since 2 is even, then the we use formula n³ª to calculate the result. It equals 3 to the (3 × 2)th power, which can be calculated as (3²)³ = 9³ = 81 × 9 = 729.
(3 # 3) corresponds to (n # a), where n = 3, a = 3. Since 3 is odd, then the we use formula n²ª to calculate the result. It equals 3 to the (2 × 3)th power, which can be calculated as (3²)³ = 9³ = 81 × 9 = 729.
Therefore (2 # 3) + (3 # 2) – (3 # 3) = 64 + 729 – 729 = 64.
