Mathematics Question on general and middle terms

Question

The coefficient of $x^{-6}$ , in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$ , is______

Accepted Answer

(54x+2x25)9
Now, Tr+1=9Cr⋅(54x)9−r(2x25)r
=9Cr⋅(54)9−r(25)r⋅x9−3r
Coefficient of x−6 i.e. 9−3r=−6⇒r=5
So, Coefficient of x−6=9C5(54)4⋅(25)5=5040
So, the correct answer is 5040.