https://file.aiquickdraw.com/mathbot/file/1730194696176tzhrz41l.jpg

The expression in the image appears to be:

\[
\left( \sqrt{2 \times 3^2} \right)^3
\]

To solve this, let's proceed with the steps:

1. **Simplify Inside the Square Root:**

   The expression inside the square root is \(2 \times 3^2\).

   - Calculate \(3^2 = 9\).
   - Then, \(2 \times 9 = 18\).

   So, the expression becomes:
   \[
   \left( \sqrt{18} \right)^3
   \]

2. **Evaluate the Square Root:**

   Find \(\sqrt{18}\).
   \[
   \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}
   \]

   Now, we have:
   \[
   \left(3\sqrt{2}\right)^3
   \]

3. **Cube the Expression:**

   Now, we cube \(3\sqrt{2}\):
   \[
   (3\sqrt{2})^3 = 3^3 \times (\sqrt{2})^3
   \]
   - \(3^3 = 27\)
   - \((\sqrt{2})^3 = 2^{3/2} = 2 \sqrt{2}\)

   So,
   \[
   (3\sqrt{2})^3 = 27 \times 2 \sqrt{2} = 54 \sqrt{2}
   \]

### Final Answer:
\[
\left( \sqrt{2 \times 3^2} \right)^3 = 54 \sqrt{2}
\]

Would you like further details on any step?

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### Related Questions

1. How do you simplify square roots involving products?
2. What is the process of cubing expressions with radicals?
3. How do you express powers of square roots in simplified forms?
4. Can you cube a square root directly, or are there simpler methods?
5. How does exponentiation distribute over multiplication in expressions?

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### Tip

Always break down complex expressions into smaller, manageable steps to avoid calculation errors.

Evaluate \(\left( \sqrt{2 \times 3^2} \right)^3\)

Learn how to evaluate \((\sqrt{2 \times 3^2})^3\) with a detailed, step-by-step breakdown. This problem involves simplifying radicals and using exponentiation, covering key mathematical concepts for high school students in Grades 9-12.

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