Multiply the two numbers without using the powers of 10. For example, if you have 3.45 x 10^4 multiplied by 4.23 x 10^-2, multiply 3.45 by 4.23 to get 14.5935.
Move the decimal place to the right or left as needed to get a number between 1 and 10. In this example, the decimal place is moved one place to the left to change from 14.5935 to 1.45935.
Add the powers of 10. In this example, the powers of 10 are "4" and "-2" so add 4 plus -2 to get 2.
Add the number of times you moved the decimal place to the left in Step 2. If you moved it to the right, subtract that number. In this example, since you moved it one place to the right, add 1 to 2 to get 3.
Plug in the result as the new power of 10. In this example, since the result equals 3, the new power will be 10^3.
Combine the Step 2 result times the Step 3 result to find the product of the two numbers in scientific notation. Completing this example, combine 1.45935 with 10^3 to find the product equals 1.45935 x 10^3.