https://file.aiquickdraw.com/mathbot/file/1727628362221prwvarib.jpg

The expression in the image is:

\[
\frac{\sqrt[3]{48} \cdot \sqrt[3]{12}}{\sqrt[3]{9}}
\]

Let's break this down step by step:

### Step 1: Combine the terms inside the cube roots in the numerator
Using the property of radicals that \(\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}\), we can combine the terms in the numerator:

\[
\sqrt[3]{48} \cdot \sqrt[3]{12} = \sqrt[3]{48 \cdot 12}
\]

Now calculate \(48 \cdot 12\):

\[
48 \cdot 12 = 576
\]

So, the expression becomes:

\[
\frac{\sqrt[3]{576}}{\sqrt[3]{9}}
\]

### Step 2: Simplify the cube root of the fraction
Using the property \(\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}}\), we can combine the radicals:

\[
\sqrt[3]{\frac{576}{9}}
\]

Now simplify \(\frac{576}{9}\):

\[
\frac{576}{9} = 64
\]

Thus, the expression becomes:

\[
\sqrt[3]{64}
\]

### Step 3: Find the cube root of 64
We know that:

\[
\sqrt[3]{64} = 4
\]

### Final Answer:
\[
4
\]

Would you like more details or have any questions?

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Here are 5 related questions to practice:

1. Simplify \(\sqrt[3]{8} \cdot \sqrt[3]{27}\).
2. What is the cube root of 125?
3. Simplify \(\frac{\sqrt[3]{32}}{\sqrt[3]{4}}\).
4. Find the value of \(\sqrt[3]{216}\).
5. How do you simplify \(\sqrt[3]{16 \cdot 81}\)?

**Tip:** Remember, when multiplying or dividing cube roots, you can combine the values under a single radical before simplifying!

Simplify the expression: (cube root of 48) * (cube root of 12) / (cube root of 9)

Learn how to simplify the expression involving cube roots: (cube root of 48) * (cube root of 12) / (cube root of 9). This problem covers radical simplification, cube root properties, and step-by-step solution for students in Grades 8-10.

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