To solve this equation, we can first simplify the right side of the equation:

(1/2)^x (16/17)^x = (3/2)^3
(1/2)^x (16/17)^x = 27/8

Now, we can rewrite the left side of the equation as a single base:

(1/2)^(x) (16/17)^x = (1/2 16/17)^x
= (8/17)^x = 27/8

Now, we can rewrite both sides of the equation with the same base:

(8/17)^x = 27/8
8/17 = (27/8)^(1/x)

To simplify further, we can take the reciprocal of both sides:

17/8 = (8/27)^x

Now, we can rewrite this in terms of powers of 2 and 3:

17/8 = (2^3 / 3^3)^x
17/8 = (2/3)^3x

Now, we can compare the corresponding sides:

17/8 = 2/3
173 = 82
51 = 16 (False)

Therefore, the equation has no solution.