Let and be two binary operations such that a b ... - JAMB Mathematics 2023 Question

The given binary operations are:

\[a * b = a^2b\]
\[a ^ b = 2a + b\]

Now, let's evaluate \((-4 * 2) ^ (7 * -1)\):

\[(-4 * 2) = (-4)^2 \times 2 = 16 \times 2 = 32\]

\[ (7 * -1) = 7^2 \times (-1) = 49 \times (-1) = -49\]

Now, substitute these values into \(a ^ b = 2a + b\):

\[ (32) ^ (-49) = 2 \times 32 + (-49) = 64 - 49 = 15\]

So, the correct answer is 15