ANSWER
a=-2, b=3
EXPLANATION
The given equation is
[tex](a {x}^{2})( - 6 {x}^{b} ) = 12 {x}^{5} [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We simplify the left hand side to get:
[tex] - 6a {x}^{2 + b} = 12 {x}^{5} [/tex]
For this equation to be true, we must have:
-6a=12 and 2+b=5
This implies that,
a=-2 and b=3
