Let ‘ × ‘ and ‘^’ be two binary operations such that a × b = a2b and a ^ b = 2a + b. Find

JAMB Mathematics 2023 52 views

Let × and ^ be two binary operations such that a × b = a²b and a ^ b = 2a + b. Find (-4 × 2) ^ (7 × -1)

  1. 64
  2. 113
  3. 15 ✓
  4. -49

Explanation

Step 1: Evaluate -4 × 2
Using rule: a × b = a²b
-4 × 2 = (-4)² × 2
= 16 × 2
= 32

Step 2: Evaluate 7 × -1
Using rule: a × b = a²b
7 × -1 = (7)² × (-1)
= 49 × (-1)
= -49

Step 3: Rewrite the expression
Original: (-4 × 2) ^ (7 × -1)
Becomes: 32 ^ (-49)

Step 4: Evaluate 32 ^ (-49)
Using rule: a ^ b = 2a + b
32 ^ (-49) = 2(32) + (-49)
= 64 – 49
= 15

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