https://file.aiquickdraw.com/mathbot/file/1727320973248iq2v4k13.jpg

Let's solve the given expression:

\[
\left(6.6 \times 10^2\right)^2 \times \left(3 \times 10^{-4}\right)
\]

### Step-by-step solution:

1. **Square the first term**:
   \[
   \left(6.6 \times 10^2\right)^2 = (6.6^2) \times (10^2)^2 = 43.56 \times 10^4
   \]

2. **Multiply the result by \(3 \times 10^{-4}\)**:
   \[
   (43.56 \times 10^4) \times (3 \times 10^{-4}) = 43.56 \times 3 \times 10^{4 + (-4)} = 130.68 \times 10^0
   \]

   Since \(10^0 = 1\), the expression simplifies to:
   \[
   130.68
   \]

Thus, the final answer in decimal notation is **130.68**.

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Do you need more details on any step, or have any questions?

Here are 5 related questions for practice:
1. What is \((5 \times 10^3)^2 \times (4 \times 10^{-2})\) in decimal notation?
2. Simplify \((7 \times 10^1)^2 \times (2 \times 10^{-3})\).
3. How would you approach \((4.5 \times 10^3) \times (6 \times 10^{-5})\)?
4. Can you calculate \((2.3 \times 10^2) \times (9 \times 10^{-1})\)?
5. What is the result of \((1.5 \times 10^4) \times (8 \times 10^{-2})\)?

**Tip**: When multiplying numbers in scientific notation, add the exponents of \(10\), and handle the numerical coefficients separately.

Perform the following operation and express the answer in decimal notation: ((6.6 * 10^2)^2) * (3 * 10^-4)

Learn how to solve the expression ((6.6 * 10^2)^2) * (3 * 10^-4) with detailed steps. This solution demonstrates key concepts like exponentiation and scientific notation, suitable for students in Grades 8-10.

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