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

The given binary operations are:

$$a\ast b=a^{2}b$$
$$a^b=2a+b$$

Now, let's evaluate $(-4\ast 2{)}^{(}7\ast -1)$:

$$(-4\ast 2)=(-4{)}^2\times 2=16\times 2=32$$

$$(7\ast -1)=7^2\times (-1)=49\times (-1)=-49$$

Now, substitute these values into $a^b=2a+b$:

$$(32{)}^{(}-49)=2\times 32+(-49)=64-49=15$$

So, the correct answer is 15