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

(4/5)^x^2 (25/64)^x^2 = (4/5 25/64)^x^2
= (1/2)^x^2

Now we have:

(1/2)^x^2 = 625/65536

Next, we can rewrite 625/65536 as (25/256)^2:

(1/2)^x^2 = (25/256)^2

Now we can equate the exponents:

x^2 = 2

Taking the square root of both sides, we get:

x = ±√2

Therefore, the solutions to the equation are x = √2 and x = -√2.