1. Multiply the coefficients:

8.4 * 4.2 = 35.28

2. Add the exponents:

10⁸ * 10³ = 10¹¹

3. Combine the results:

35.28 * 10¹¹

4. Adjust for scientific notation:

Since the coefficient needs to be between 1 and 10, we move the decimal one place to the left. This means we increase the exponent by 1.

3.528 x 10¹²

Therefore, the product of 8.4 x 10⁸ and 4.2 x 10³ in scientific notation is 3.528 x 10¹².