Multiply numbers in scientific notation: compute (6 × 10^3)(5 × 10^5), combine coefficients and exponents correctly, and report the product.

Introduction / Context:
Scientific notation simplifies multiplication and division of very large or very small numbers by separating coefficient arithmetic from exponent arithmetic. This problem reinforces multiplying coefficients and adding exponents, then optionally normalizing the result.

Given Data / Assumptions:

• (6 × 10^3) multiplied by (5 × 10^5).
• Standard rule: (a × 10^m)(b × 10^n) = (a * b) × 10^(m + n).
• Normalization to a 1–10 coefficient is optional if the numerical value is correct.

Concept / Approach:

Multiply the numeric coefficients first, then add the exponents. Finally, compare with the options; some options present the same value with an unnormalized coefficient and a different exponent, which can still be correct.

Step-by-Step Solution:

Verification / Alternative check:

As decimals: 6,000 × 500,000 = 3,000,000,000 = 3 × 10^9 = 30 × 10^8. This confirms the selected option.

Why Other Options Are Wrong:

3 × 10^8 is too small by a factor of 10. 300 × 10^9 equals 3 × 10^11 (far too large). 3,000 × 10^7 equals 3 × 10^10 (also too large).

Common Pitfalls:

Adding instead of multiplying coefficients; mis-adding exponents; over-normalizing and then mismatching to given answer formats.

Final Answer:

30 × 10^8