To solve the expression \( (3 \times 10^5) \times (4 \times 10^3) \) and find its equivalent in standard form, let's break it down step-by-step. ### Step 1: Multiply the Coefficients First, we need to multiply the numerical coefficients (the numbers in front of the powers of ten): \[ 3 \times 4 = 12 \] ### Step 2: Add the Exponents Next, we multiply the powers of ten. When multiplying powers of ten, we add the exponents: \[ 10^5 \times 10^3 = 10^{5+3} = 10^8 \] ### Step 3: Combine the Results Now, we combine the results from Steps 1 and 2: \[ (3 \times 10^5) \times (4 \times 10^3) = 12 \times 10^8 \] ### Step 4: Convert to Standard Form Standard form requires that the coefficient (the number in front) is between 1 and 10. The number \( 12 \) is not in this range, so we need to convert it: \[ 12 = 1.2 \times 10^1 \] Now, we can substitute this back into our expression: \[ 12 \times 10^8 = (1.2 \times 10^1) \times 10^8 \] Using the property of exponents again, we combine the powers of ten: \[ (1.2 \times 10^1) \times 10^8 = 1.2 \times 10^{1+8} = 1.2 \times 10^9 \] However, we made a mistake in our previous step. The correct conversion should be: \[ 12 \times 10^8 = 1.2 \times 10^9 \] But we need to express \( 12 \times 10^8 \) in a way that fits the options given. ### Step 5: Review the Options Now, let's look at the options provided: - **A. \( 12 \times 10^8 \)**: This is the original expression we calculated. - **B. \( 12 \times 10^7 \)**: This is incorrect because it does not match our calculation. - **C. \( 1.2 \times 10^8 \)**: This is incorrect because we have \( 1.2 \times 10^9 \). - **D. \( 1.2 \times 10^7 \)**: This is also incorrect. ### Conclusion The correct answer is actually \( 12 \times 10^8 \), which is option A. ### Summary of Key Points - When multiplying numbers in scientific notation, multiply the coefficients and add the exponents. - Ensure the coefficient is between 1 and 10 for standard form. - If the coefficient exceeds 10, convert it to the appropriate form by adjusting the exponent. - Always double-check your calculations to ensure accuracy. ### Final Note The recorded correct option C is incorrect based on the calculations provided. The correct answer is A, \( 12 \times 10^8 \).