Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10015
100 superscript 15 baseline
10056
100 superscript 56 baseline
20015
200 superscript 15 baseline
10,00015
The correct answer is 10015.
To simplify the expression 1008 ⋅ 1007 using the Product Rule of Exponents, we add the exponents of the same base numbers.
In this case, both base numbers are 100 (10^2), so we add the exponents.
The exponent of 1008 is 2 (10^2), and the exponent of 1007 is 1 (10^1).
Adding these exponents together gives us 2 + 1 = 3.
Therefore, the simplified expression using the Product Rule of Exponents is 100^3, which is equal to 1,000,000.
Looking at the given responses:
1. 100^15 = 10,000^15 ≠ 1008 ⋅ 1007 (incorrect)
2. 100^56 = 100,000^56 ≠ 1008 ⋅ 1007 (incorrect)
3. 200^15 = 32,000,000,000,000,000 ≠ 1008 ⋅ 1007 (incorrect)
4. 10,000^15 = 1,000,000^15 ≠ 1008 ⋅ 1007 (incorrect)
None of the given responses correctly simplify the expression 1008 ⋅ 1007 using the Product Rule of Exponents.