To simplify the expression \( (3 \times 10^4) \times (2 \times 10^3) \) in standard form, we will follow a step-by-step approach. ### Step 1: Understand the Components The expression consists of two parts: - \( 3 \times 10^4 \) - \( 2 \times 10^3 \) Here, \( 3 \) and \( 2 \) are the coefficients, while \( 10^4 \) and \( 10^3 \) are the powers of ten. ### Step 2: Multiply the Coefficients First, we multiply the coefficients: \[ 3 \times 2 = 6 \] ### Step 3: Add the Exponents Next, we need to multiply the powers of ten. When multiplying numbers in scientific notation, we add the exponents: \[ 10^4 \times 10^3 = 10^{4+3} = 10^7 \] ### Step 4: Combine the Results Now, we combine the results from Steps 2 and 3: \[ (3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7 \] ### Final Result Thus, the simplified expression in standard form is: \[ 6 \times 10^7 \] ### Conclusion The correct option is **A. \( 6 \times 10^7 \)**. ### Explanation of Other Options - **B. \( 6 \times 10^8 \)**: This option is incorrect because it suggests that we added the exponents incorrectly (4 + 3 = 8 instead of 7). - **C. \( 5.1 \times 10^8 \)**: This option is incorrect as it not only has the wrong exponent but also an incorrect coefficient. The multiplication of the coefficients (3 and 2) gives 6, not 5.1. - **D. \( 6 \times 10^6 \)**: This option is incorrect because it suggests that the exponent was reduced instead of correctly adding them. The correct exponent is 7, not 6. ### Common Pitfalls - **Forgetting to add the exponents**: When multiplying powers of ten, always remember to add the exponents. - **Incorrectly multiplying coefficients**: Ensure that you multiply the coefficients accurately. - **Misinterpreting standard form**: Standard form requires the coefficient to be between 1 and 10, which is satisfied in this case. ### Revision Summary - Multiply the coefficients: \( 3 \times 2 = 6 \). - Add the exponents: \( 10^4 \times 10^3 = 10^{7} \). - Combine results: \( 6 \times 10^7 \) is the final answer. - The correct option is **A. \( 6 \times 10^7 \)**.