Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point) Responses 20015 200 superscript 15 baseline 10056 100 superscript 56 baseline 10015 100 superscript 15 baseline 10,00015
The correct answer is 10015, 100 superscript 15 baseline.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we add the exponents when multiplying numbers with the same base.
1008 = 10^3, 1007 = 10^2
Using the Product Rule of Exponents:
1008⋅1007 = (10^3)⋅(10^2) = 10^(3+2) = 10^5 = 10015
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we can multiply the base numbers (1008 and 1007) and add the exponents (1+1).
Therefore, 1008⋅1007 = 100^(1+1) * 8^(1+1).
Simplifying further, we get:
100^(1+1) = 100^2 = 10,000.
8^(1+1) = 8^2 = 64.
Multiplying the base numbers:
10,000 * 64 = 640,000.
So, the simplified expression is 640,000.
None of the provided options match the correct answer.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we must add the exponents when multiplying numbers with the same base.
In this case, the base is 10 and the exponents are 8 and 7 respectively.
Using the Product Rule of Exponents, we add the exponents:
10^8 * 10^7 = 10^(8+7) = 10^15
Therefore, the correct answer is 100⋅10^15 which can be written as 100 superscript 15 baseline.
Thus, the correct option is: 100 superscript 15 baseline.