https://file.aiquickdraw.com/mathbot/file/1730305056341zo4w3jcq.jpg

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.

Learn how to simplify the expression \( \frac{16}{\sqrt[4]{16^3}} \) using exponents and radicals. This solution explains step-by-step techniques for simplifying powers and roots, making it ideal for students in Grades 8-10.

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