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?

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.