Because to have a constant term, there must be n=0 and n=4(x/2 takes 1 time,-1/3√x takes 3 times).
N=8(x/2 takes 2 times,-1/3√x takes 6 times), and n= 12(x/2 takes 3 times,-1/3√x takes 9 times). ...
The fifth item cannot have n= 1, 4∴n=8, 12. ...
When n=8, the constant term is: (2 c8)*(x/2)2 *( 1/3√x)6 = 7.
When n= 12, the constant term is (3c12) * (x/2) 3 * (1/3 √ x) 9 = 27.5.
If n is larger, the constant term will be larger and will not appear in the option.
Of course, strictly speaking, it is necessary to write the binomial coefficient general term (kcn) * (1/2) k * (1) (n-k) to find the extreme value.
5.∵a5=5C8*(-a)^3=56∴a=- 1
∴ A0+a1+…+A8 = (1-a) 8 = 28, choose C.