To solve $(6.2 \times 10^7) \times (5 \times 10^{-3})$, follow the steps:

Step 1: Multiply the coefficients (the numbers before the powers of 10):

$6.2 \times 5 = 31$

Step 2: Add the exponents of 10 (since the base is the same, $10$):

$10^7 \times 10^{-3} = 10^{7 + (-3)} = 10^4$

Step 3: Combine the results:

$31 \times 10^4$

Step 4: Express in scientific notation (if needed):

$31 \times 10^4 = 3.1 \times 10^1 \times 10^4 = 3.1 \times 10^5$

Thus, the result is: $3.1 \times 10^5$

Would you like further details or have any questions? Here are some related questions you might find useful:

1. How do you multiply numbers in scientific notation when the exponents are the same?
2. How can we convert numbers from scientific notation to standard form?
3. What is the rule for dividing numbers in scientific notation?
4. How does the decimal point shift when moving between scientific notation and standard form?
5. Can you explain how to handle negative exponents in scientific notation?

Tip: Always check if your result is in proper scientific notation, meaning the coefficient is between 1 and 10.