ANSWER
The correct answer is B
[tex] \frac{4b}{ {a}^{2} } [/tex]
EXPLANATION
The given exponential expression is
[tex]4 {a}^{ - 2} b[/tex]
We can rewrite this as,
[tex]4b \times {a}^{ - 2} [/tex]
We need to simplify to obtain a positive index, so we apply the following property,
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
This implies that,
[tex]4b \times {a}^{ - 2} = 4b \times \frac{1}{ {a}^{2} } [/tex]
This will finally simplify to,
[tex]4b \times {a}^{ - 2} =\frac{4b}{ {a}^{2} } [/tex]
Therefore the correct answer is B
