https://file.aiquickdraw.com/mathbot/file/1727013779996h6zmk7o0.jpg

The expression shown in the image is:

\[
1.2 \cdot 10^{-5} \cdot 6 \cdot 10^{-4} \cdot 5 \cdot 10^{-3}
\]

Let’s simplify this step by step:

### Step 1: Combine the numerical coefficients
The numerical values to multiply are \(1.2 \cdot 6 \cdot 5\).

\[
1.2 \cdot 6 = 7.2
\]
\[
7.2 \cdot 5 = 36
\]

### Step 2: Combine the powers of 10
Next, we combine the exponents of 10. We add the exponents because we are multiplying powers of 10:

\[
10^{-5} \cdot 10^{-4} \cdot 10^{-3} = 10^{(-5 - 4 - 3)} = 10^{-12}
\]

### Step 3: Final result
Now, combine the result from the numerical coefficients and the powers of 10:

\[
36 \cdot 10^{-12}
\]

This is the simplified form of the given expression.

Would you like any further details or clarifications?

Here are 5 related questions to expand on this:
1. How do you multiply powers with the same base?
2. What would happen if the exponents were positive?
3. How can you express the final result in scientific notation?
4. What is the rule for dividing powers with the same base?
5. How do you simplify an expression that involves both multiplication and division of powers?

**Tip:** When multiplying powers of 10, always remember to add their exponents if the base is the same!

Simplify the expression 1.2 * 10^(-5) * 6 * 10^(-4) * 5 * 10^(-3).

Learn how to simplify the expression 1.2 * 10^(-5) * 6 * 10^(-4) * 5 * 10^(-3) step-by-step. This problem focuses on scientific notation, exponents, and multiplication, suitable for students in Grades 9-12.

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