The simplified result of the expression $\frac{2^4 \cdot 4}{\sqrt{2}}$ is:

$32\sqrt{2}$

Would you like further explanation on how it was simplified, or do you have any other questions?

Here are five related questions to explore further:

1. How can you rationalize a denominator with a square root?
2. What are the properties of exponents and roots used in this problem?
3. How does multiplying by $\sqrt{2}$ affect the result?
4. Can you express $32\sqrt{2}$ as a decimal approximation?
5. What are other ways to simplify radical expressions?

Tip: When simplifying expressions with square roots in the denominator, it's often useful to rationalize the denominator by multiplying by the appropriate radical.