To solve this expression, first simplify each part separately:

2^8 = 256
7^2 = 49
4/14 = 2/7

Then the expression becomes:

256 49 (2/7)^4

Now, evaluate (2/7)^4:

(2/7)^4 = (2^4) / (7^4) = 16 / 2401 ≈ 0.006664

Finally, multiply 256 49 0.006664:

256 49 0.006664 ≈ 84.512

Therefore, the result of the expression 2^8 (7^2) 4/14^4 is approximately 84.512.