We are asked to evaluate the expression $4^4 / 7 \sqrt[3]{2^6}$.

1. Problem Description

We are asked to evaluate the expression $4^4 / 7 \sqrt[3]{2^6}$.

2. Solution Steps

First, let's evaluate $4^4$:

$4^4 = 4 \times 4 \times 4 \times 4 = 16 \times 16 = 256$

Next, we evaluate $\sqrt[3]{2^6}$.

$\sqrt[3]{2^6} = (2^6)^{1/3} = 2^{6 \times (1/3)} = 2^{6/3} = 2^2 = 4$

Now we can rewrite the original expression:

$4^4 / 7 \sqrt[3]{2^6} = 256 / (7 \times 4)$

Then we evaluate the denominator:

$7 \times 4 = 28$

Finally, we evaluate the fraction:

$256 / 28 = 64 / 7$

3. Final Answer

64/7