To simplify this expression, we first simplify the powers:

4^10 = 2^20
(2^4)^3 = 2^12
4^2 = 2^4
(2^2)^12 = 2^24

Now we substitute the simplified powers back into the expression:

2^20 2^12 / 2^4 2^24
= 2^(20+12) / 2^4 2^24
= 2^32 / 2^4 2^24
= 2^(32-4) 2^24
= 2^28 2^24
= 2^(28+24)
= 2^52

Therefore, 4^10 (2^4)^3 / 4^2 (2^2)^12 simplifies to 2^52.