Final answer:
To multiply two numbers in scientific notation, multiply the base numbers and add the exponents. The result is normalized to scientific notation, giving -2.856 x 10¹.
Step-by-step explanation:
The calculation of the product between two numbers in scientific notation, (-3.4 x 10⁻⁷) x (8.4 x 10⁵), involves multiplying the base numbers (-3.4 and 8.4) and adding the exponents of ten (-7 and 5). First, multiply the base numbers: -3.4 x 8.4 = -28.56. Next, add the exponents: -7 + 5 = -2. Therefore, the result in scientific notation is -28.56 x 10². However, scientific notation requires a base number between 1 and 10, so the result must be normalized yielding -2.856 x 10¹.