To solve this equation, we can simplify the expression on the left side of the equation by using the properties of exponents.

First, we can rewrite 2^7x as (2^4x)(2^3x) since 7x = 4x + 3x.

Now, we can substitute this expression into the equation:

(2^4x)(2^3x) / 2^4x = 64

Next, we can simplify the expression by canceling out the common factor of 2^4x:

2^3x = 64

Now, we can rewrite 64 as 2^6 since 2^6 = 64:

2^3x = 2^6

Since the bases are the same, we can equate the exponents:

3x = 6

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 6/3

x = 2

Therefore, the solution to the equation is x = 2.