https://file.aiquickdraw.com/mathbot/file/1727010802298ykdnwyir.jpg

The expression in the image is:

\[
\left( 2 \cdot 10^{-3} \right)^2
\]

Let's solve it step by step:

### Step 1: Square the base
We need to square both factors inside the parentheses. The expression can be split as follows:

\[
\left( 2 \cdot 10^{-3} \right)^2 = (2^2) \cdot \left( 10^{-3} \right)^2
\]

### Step 2: Square the individual components
- \( 2^2 = 4 \)
- \( \left( 10^{-3} \right)^2 = 10^{-6} \) (Since when you raise a power to another power, you multiply the exponents: \( (-3) \times 2 = -6 \))

### Step 3: Multiply the results
Now, multiply the squared components:

\[
4 \cdot 10^{-6} = 4 \times 10^{-6}
\]

So, the simplified result is:

\[
4 \times 10^{-6}
\]

This is the final answer.

Would you like more details on any part of the solution? Here are some related questions:

1. What happens when multiplying exponents with the same base?
2. How does squaring a negative exponent work?
3. Can you explain how powers of 10 are simplified when multiplied?
4. How do you handle more complex expressions with multiple terms involving exponents?
5. What is the significance of scientific notation when working with small or large numbers?

### Tip:
When squaring an expression, make sure to apply the exponent to each term inside the parentheses separately.

This problem explores exponentiation with scientific notation. Learn how to square the expression (2 ⋅ 10^(-3))^2, involving exponents and powers of 10. Follow the step-by-step solution, ideal for students in Grades 8-10.

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