Final answer:
The product of two expressions in scientific notation should be calculated by multiplying the coefficients and adding the exponents of 10, resulting in an answer in scientific notation that is rounded and formatted accordingly.
Step-by-step explanation:
The student has asked regarding the product of two expressions, which seems to entail variables and scientific notation. Since the expressions provided in the question are not clear, we'll use the examples given in the additional context to work with expressing products in scientific notation. According to the context provided, performing the appropriate operation and expressing the answer in scientific notation can be seen in example 2.2.3, where (6.022 × 10²³) is multiplied by (6.42 × 10⁻²), resulting in a product that should be represented in scientific notation.
For proper multiplication in scientific notation, we multiply the coefficients (the numbers before the exponentiation) and add the exponents of the 10s if the base is the same, applying the rule (xa)b = xa.b:
6.022 × 6.42 = 38.68124
(10²³)(10⁻²) = 10²³+(-2) = 10²¹
So the answer is 3.868124 × 10²¹, which should then be rounded and formatted in scientific notation, such as many of the examples provided that follow a similar pattern.