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To solve this problem, let's calculate \((4 \times 10^{-2}) \times (6 \times 10^5)\) and express the result in scientific notation.

### Step-by-Step Solution
1. **Multiply the coefficients (numbers):**  
   \(4 \times 6 = 24\).

2. **Apply the properties of exponents:**  
   \(10^{-2} \times 10^5 = 10^{(-2 + 5)} = 10^3\).

3. **Combine these results:**  
   \(24 \times 10^3\).

4. **Express in scientific notation:**  
   Since scientific notation requires a single non-zero digit to the left of the decimal point, we rewrite \(24 \times 10^3\) as:
   \[
   2.4 \times 10^4
   \]

### Final Answer
\[
2.4 \times 10^4
\]

Would you like further clarification on any of these steps, or do you have any other questions?

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Here are some related questions to expand your understanding:

1. What would happen if one of the exponents was negative and larger in absolute value?
2. How would you multiply three terms in scientific notation, like \((3 \times 10^2) \times (4 \times 10^{-1}) \times (2 \times 10^3)\)?
3. Can you explain the process for dividing numbers in scientific notation?
4. How would you convert a number in standard form, like 3500, into scientific notation?
5. What are some common mistakes to avoid when working with exponents in scientific notation?

**Tip:** Remember that when multiplying powers of 10, you can add the exponents, and when dividing, you subtract them. This can save time and simplify calculations.

This guide explains how to multiply numbers in scientific notation with a step-by-step solution for (4 × 10^(-2)) × (6 × 10^5). Learn how to apply exponent rules and express the result in proper scientific notation. Ideal for students in Grades 8-10.

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