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To solve the given expression \(\sqrt[4]{9x^3} \cdot \sqrt[4]{5}\), we can use the product rule for radicals.

### Step-by-Step Solution

1. **Combine the Radicals Using the Product Rule**:
   \[
   \sqrt[4]{9x^3} \cdot \sqrt[4]{5} = \sqrt[4]{(9x^3) \cdot 5}
   \]

2. **Multiply Inside the Radical**:
   \[
   = \sqrt[4]{45x^3}
   \]

3. **Simplify, if Possible**:
   Since \(45x^3\) does not have any perfect fourth powers as factors, this is as simplified as it can get under a fourth root. 

### Final Answer
\[
\sqrt[4]{45x^3}
\]

Would you like further details on this solution, or do you have any questions?

### Additional Practice Questions

1. How would you simplify \(\sqrt[3]{8x^6} \cdot \sqrt[3]{4}\)?
2. How can you rewrite \(\sqrt[5]{32x^5}\) in terms of exponents?
3. If \(y = \sqrt[4]{x^2}\), what is the simplified form of \(y\)?
4. What is \(\sqrt[4]{16x^4}\)?
5. How can you combine and simplify \(\sqrt[6]{64x^5} \cdot \sqrt[6]{2x}\)?

### Tip
When multiplying radicals with the same root, you can combine them into a single radical by multiplying the terms inside the root.

Use the product rule to multiply. Assume that all variables represent positive real numbers. \(\sqrt[4]{9x^3} \cdot \sqrt[4]{5}\).

Learn how to simplify the expression \(\sqrt[4]{9x^3} \cdot \sqrt[4]{5}\) by applying the product rule for radicals. This solution provides a step-by-step approach, ideal for students in Grades 9-11.

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