Answer:
[tex]\frac{y}{2(x+3)}[/tex]
Step-by-step explanation:
We are given exponential expression [tex]4y(8y+24)^{-1}[/tex].
First we need to remove that negative exponent from the (8y+24).
According to negative exponent rule, the expression (8y+24) would go in the bottom of 4y and it would become positive exponent.
Therefore,
[tex]4y(8y+24)^{-1}[/tex] =[tex]\frac{4y}{8y+24}[/tex]
Factoring out gcf 8 in bottom expression 8y+24, we get 8(x+3).
Therefore,
[tex]\frac{4y}{8(x+2)}[/tex]
Dividing top and bottom by 4, we get
[tex]\frac{y}{2(x+3)}[/tex]
Therefore, [tex]\frac{y}{2(x+3)}[/tex] is the simplest form of the given expression [tex]4y(8y+24)^{-1}[/tex].
