use scientific notation to multiply the following two numbers. Express the answer using scientific notation; retain all nonzero decimal places.

(8.1*10^8)*(4.2*10^3)

(8.1)(4.2) 10^(8+3)

34.02 * 10^11

3.402 * 10^12

To multiply numbers in scientific notation, you need to multiply the two decimal parts and multiply the two exponent parts separately. Then, you can combine the results to express the answer in scientific notation. Let's go step by step:

Step 1: Multiply the decimal parts: 8.1 * 4.2 = 34.02

Step 2: Multiply the exponent parts: 10^8 * 10^3 = 10^(8+3) = 10^11

Step 3: Combine the results: 34.02 * 10^11

To express the answer in scientific notation and retain all nonzero decimal places, we can write it as 3.402 * 10^12.