To find the middle term of the expansion of (2x/y^3)^12, we need to first determine the number of terms in the expansion.
Using the formula for the binomial theorem, we know that the number of terms in the expansion of (2x/y^3)^12 is 13.
Now, to find the middle term, we need to find the term that is in the middle of the expansion. Since there are 13 terms in the expansion, the middle term is the 7th term.
The general term of the expansion is given by:
T(r+1) = (12 C r) (2x)^r (y^-3)^(12-r)
So, the 7th term is:
T(8) = (12 C 7) (2x)^7 (y^-3)^(5)
Simplifying this expression, we get:
T(8) = (792) (128x^7 / y^15)
Therefore, the middle term of the expansion is 792(128x^7/y^15)