https://file.aiquickdraw.com/mathbot/file/1726871941037zo7shmx0.jpg

The equation in the image is:

\[
(6 \times 10^{-6}) \times (3 \times 10^{-2}) = ?
\]

We can solve this by applying the rules of scientific notation. Specifically, when multiplying numbers in scientific notation:

\[
(a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n}
\]

Now, let's calculate:

1. Multiply the base numbers:  
   \( 6 \times 3 = 18 \)

2. Add the exponents:  
   \( -6 + (-2) = -8 \)

So, the result is:

\[
18 \times 10^{-8}
\]

Since \(18\) is not between 1 and 10, we convert it into proper scientific notation:

\[
18 \times 10^{-8} = 1.8 \times 10^{-7}
\]

Thus, the simplified answer in scientific notation is:

\[
1.8 \times 10^{-7}
\]

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:
1. How do you convert between scientific notation and standard form?
2. What is the rule for multiplying two numbers in scientific notation?
3. How would the process differ if we were dividing instead of multiplying?
4. What are the rules for adding or subtracting numbers in scientific notation?
5. How can you quickly determine if a number is in proper scientific notation?

**Tip:** When multiplying numbers in scientific notation, remember to handle the base numbers and the powers of 10 separately!

Learn how to multiply numbers in scientific notation using the example (6 × 10^(-6))(3 × 10^(-2)). This step-by-step guide covers key concepts such as multiplying base numbers and adding exponents. Suitable for students in Grades 9-12.

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