https://file.aiquickdraw.com/mathbot/file/17271005701789fk25x7k.jpg

To solve this problem, we are tasked with finding the simplified product of:

\[
\sqrt[3]{15} \cdot \sqrt[3]{9}
\]

### Step-by-step solution:

1. **Understanding the expression**: Both terms are cube roots, so we can combine them using the property of radicals:

   \[
   \sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}
   \]

2. **Applying this property**: 

   \[
   \sqrt[3]{15} \cdot \sqrt[3]{9} = \sqrt[3]{15 \cdot 9}
   \]

3. **Multiplying inside the cube root**:

   \[
   15 \times 9 = 135
   \]

   Thus, the expression becomes:

   \[
   \sqrt[3]{135}
   \]

4. **Simplifying the cube root**: We can try to factor 135 to see if any factors are perfect cubes.

   \[
   135 = 3^3 \times 5
   \]

   Therefore:

   \[
   \sqrt[3]{135} = 3 \sqrt[3]{5}
   \]

Thus, the simplified product is:

\[
3 \sqrt[3]{5}
\]

The correct answer is: **\( 3 \sqrt[3]{5} \)**.

Would you like more details on any of the steps?

Here are 5 related questions you might find helpful:

1. How do you simplify expressions involving cube roots in general?
2. What is the difference between square roots and cube roots when simplifying products?
3. How can you determine if a number inside a radical can be simplified?
4. What are the properties of radicals when multiplying and dividing them?
5. How do you simplify higher-order radicals (e.g., fourth or fifth roots)?

**Tip:** When simplifying products involving radicals, always check if the numbers can be factored into powers that match the index of the root, as this helps with simplification.

Find the simplified product. Cube root of 15 multiplied by cube root of 9.

Learn how to simplify the product of cube roots of 15 and 9 using radical properties. This step-by-step solution covers important algebraic concepts for Grades 8-10 students.

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