Final answer:
To find the product, multiply the digit terms and add the exponents of the exponential terms. The product of 3.2 × 10³ times 2 × 10² is 6.4 × 10³5.
Step-by-step explanation:
To find the product and write the answer in exponential form, we will follow the multiplication of exponentials rule. According to this rule, we should multiply the digit terms in the usual way and add the exponents of the exponential terms. Using the example provided, we can express 3.2 × 10³ times 2 × 10² as 3.2 × 2 × 10³ × 10².
First, we multiply the digit terms: 3.2 × 2 = 6.4. We then add the exponents of the exponential terms, since they have the same base (10): 10³ × 10² = 10³5, because 3 + 2 = 5. Therefore, the product in exponential form is 6.4 × 10³5.