To simplify the expression \( (3 \times 10^4) \times (2 \times 10^3) \) in standard form, let's break it down step-by-step. ### 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 Answer Thus, the simplified expression in standard form is: \[ 6 \times 10^7 \] ### Correct Option The correct option is **A. \( 6 \times 10^7 \)**. ### Explanation of Other Options - **B. \( 6 \times 10^6 \)**: This option is incorrect because it suggests that the exponent of ten should be \( 6 \) instead of \( 7 \). This would imply that we did not correctly add the exponents when multiplying the powers of ten. - **C. \( 5.5 \times 10^7 \)**: This option is incorrect because it uses \( 5.5 \) as the coefficient instead of \( 6 \). The multiplication of the coefficients \( 3 \) and \( 2 \) gives \( 6 \), not \( 5.5 \). - **D. \( 5.5 \times 10^6 \)**: This option is incorrect for the same reasons as options B and C. It incorrectly uses both the coefficient \( 5.5 \) and the exponent \( 6 \), which do not match the results of our calculations. ### Common Pitfalls - **Forgetting to add exponents**: When multiplying powers of ten, always remember to add the exponents. - **Incorrectly multiplying coefficients**: Ensure that you multiply the coefficients correctly; small mistakes can lead to incorrect answers. - **Misinterpreting standard form**: Standard form requires that the coefficient is between \( 1 \) and \( 10 \). In this case, \( 6 \) is valid. ### Revision Summary - To multiply numbers in scientific notation, multiply the coefficients and add the exponents. - The expression \( (3 \times 10^4) \times (2 \times 10^3) \) simplifies to \( 6 \times 10^7 \). - Always check your calculations for both coefficients and exponents to avoid common mistakes. - The correct answer is **A. \( 6 \times 10^7 \)**.