Final answer:
The product of 10^3 and 10^4 is 10^7, because when multiplying exponents with the same base, the exponents are added together. Scientific notation uses this rule to simplify arithmetic involving very large or very small numbers.
Step-by-step explanation:
The student's question indicates a misunderstanding about the multiplication of powers of 10. When multiplying exponents with the same base, you add the exponents together. Thus, for the expression 10^3 × 10^4, you add the exponents 3 and 4 to get 7. Therefore, the correct answer is 10^7, not 10^3 or 10^28. Applying the rule of multiplying exponentiated quantities, the correct representation is 10^{3+4} = 10^7, which confirms the product as 10,000,000 and not 1,000 or a number with 28 zeros after it.
Scientific notation simplifies arithmetic, especially when dealing with large or small numbers. For instance, a large number like 1,372,568 is more conveniently written as 1.372568 × 10^6, while multiplication of powers of 10 only requires adding the exponents. An example to highlight is (3 × 10^5) × (2 × 10^0) resulting in 6 × 10^5.
This concept is also critical in applications like scientific notation, where it enables easy multiplication and division of very large or very small numbers.