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The problem asks to work out:

\[
(2 \times 10^3) \times (3 \times 10^5)
\]

and provide the answer in standard form. Let's break it down step by step:

### Step 1: Multiply the coefficients
We first multiply the numbers 2 and 3:

\[
2 \times 3 = 6
\]

### Step 2: Multiply the powers of 10
Next, we multiply the powers of \( 10 \), which follows the rule of exponents:

\[
10^3 \times 10^5 = 10^{3+5} = 10^8
\]

### Step 3: Combine the results
Now we combine the results of the multiplication:

\[
(2 \times 10^3) \times (3 \times 10^5) = 6 \times 10^8
\]

### Final Answer:
The answer in standard form is:

\[
6 \times 10^8
\]

Would you like more details or have any questions about this solution?

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Here are five related questions to expand your understanding:
1. How do you handle multiplication of numbers in scientific notation with different powers of 10?
2. What happens when you multiply a number by \(10^0\)?
3. How would you divide two numbers in scientific notation, such as \( (4 \times 10^6) \div (2 \times 10^2) \)?
4. How can you convert a large number like \( 6 \times 10^8 \) back into decimal form?
5. What is the rule for adding exponents when multiplying powers of the same base?

**Tip**: Always handle the coefficients and the powers of 10 separately when performing multiplication in scientific notation!

Work out (2 × 10^3) × (3 × 10^5). Give your answer in standard form.

Solve the problem of multiplying numbers in scientific notation: (2 × 10^3) × (3 × 10^5). This example shows how to handle multiplication of exponents and standard form. Suitable for students in Grades 8-10.

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