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The expression you provided is:

\[
(7 \times 10^2) \times (3 \times 10^1)
\]

### Steps to solve:

1. **Multiply the coefficients**: \( 7 \times 3 = 21 \)
2. **Add the exponents**: For \( 10^2 \times 10^1 \), you add the exponents: \( 2 + 1 = 3 \).

So, the result is:

\[
21 \times 10^3
\]

To express this in proper scientific notation, we rewrite \( 21 \) as \( 2.1 \times 10^1 \), and then combine the powers of 10:

\[
2.1 \times 10^4
\]

Thus, the final answer in scientific notation is:

\[
\boxed{2.1 \times 10^4}
\]

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How do you multiply numbers in scientific notation in general?
2. Why do we add exponents when multiplying powers of 10?
3. How would you divide two numbers in scientific notation?
4. What if one number had a negative exponent, how would the result change?
5. Can you convert scientific notation back into standard form?

**Tip**: When working with scientific notation, always ensure the coefficient (the number in front) is between 1 and 10 for correct scientific notation format.

Learn how to solve a multiplication problem in scientific notation: (7 × 10^2) × (3 × 10^1). This problem covers the multiplication of powers of 10 and rules for adding exponents. Ideal for students in Grades 6-8.

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