To solve the expression given in the image, we have:

$\frac{16}{\sqrt[4]{16^3}}$

Let's simplify step-by-step:

1. Simplify the denominator:
   The denominator is $\sqrt[4]{16^3}$, which is the fourth root of $16^3$.

2. Rewrite 16 in terms of powers of 2:
   We know that $16 = 2^4$, so $16^3 = (2^4)^3 = 2^{12}$.

3. Rewrite the fourth root:
   The fourth root of $2^{12}$ is $2^{12/4} = 2^3 = 8$.

   So, $\sqrt[4]{16^3} = 8$.

4. Substitute back into the expression:
   Now we have: $\frac{16}{8} = 2$

Thus, the simplified answer is:

$\boxed{2}$

Would you like more details on any step or have any questions?

Follow-up Questions:

1. What is the general rule for simplifying roots of powers?
2. How would this problem change if we used a square root instead of a fourth root?
3. What happens if we increase the exponent from 3 to another power?
4. How can we apply this approach to other bases (not just powers of 2)?
5. How can you simplify other similar expressions with different root indices?

Tip:

When dealing with roots of powers, try to express the base in terms of smaller prime factors (like expressing 16 as $2^4$) to simplify your calculations.