To simplify the expression \( (3 \times 10^4) \times (2 \times 10^3) \) into standard form, we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Understand the Components The expression consists of two parts: - \( 3 \times 10^4 \): This means 3 multiplied by \( 10^4 \) (which is 10,000). - \( 2 \times 10^3 \): This means 2 multiplied by \( 10^3 \) (which is 1,000). ### Step 2: Multiply the Coefficients First, we multiply the numerical coefficients (the numbers in front): - Coefficients: \( 3 \) and \( 2 \) - Calculation: \[ 3 \times 2 = 6 \] ### Step 3: Multiply the Powers of Ten Next, we multiply the powers of ten. When multiplying powers of ten, we add the exponents: - Exponents: \( 4 \) and \( 3 \) - Calculation: \[ 10^4 \times 10^3 = 10^{4+3} = 10^7 \] ### Step 4: Combine the Results Now, we combine the results from Steps 2 and 3: - Result: \[ 6 \times 10^7 \] ### Final Answer Thus, the simplified expression in standard form is: \[ 6 \times 10^7 \] ### Why the Other Options Are Incorrect Now, let's analyze the other options to understand why they are incorrect: - **Option A: \( 6 \times 10^7 \)** - This is actually the correct answer, so it is not incorrect. - **Option B: \( 6 \times 10^8 \)** - This option suggests that we added the exponents incorrectly. The correct addition of the exponents is \( 4 + 3 = 7 \), not \( 8 \). - **Option C: \( 6 \times 10^6 \)** - This option suggests that we subtracted the exponents instead of adding them. The correct operation is to add the exponents when multiplying powers of ten. - **Option D: \( 5 \times 10^7 \)** - This option incorrectly states the coefficient. The correct coefficient from multiplying \( 3 \) and \( 2 \) is \( 6 \), not \( 5 \). ### Summary of Key Points - To multiply numbers in scientific notation, multiply the coefficients and add the exponents of the powers of ten. - The correct simplification of \( (3 \times 10^4) \times (2 \times 10^3) \) is \( 6 \times 10^7 \). - Be careful with the operations on exponents: add when multiplying and subtract when dividing. - Always double-check your calculations to avoid simple arithmetic errors. This thorough breakdown should help you understand how to simplify expressions in scientific notation and avoid common pitfalls.