Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10,00015
10,000 superscript 15 baseline
10056
100 superscript 56 baseline
10015
100 superscript 15 baseline
20015
1008⋅1007 can be simplified using the product rule of exponents as follows:
1008⋅1007 = (10^3⋅2^3)⋅(10^3⋅7) = 10^(3+3)⋅2^3⋅7 = 10^6⋅8⋅7
Therefore, the correct answer is: 10,000^15
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we add the exponents when multiplying powers with the same base.
Let's break down the steps:
First, we can write 1008 as 10^3 and 1007 as 10^3.
Using the Product Rule of Exponents, we can simply add the exponents: 10^3 * 10^3 = 10^(3+3) = 10^6.
Therefore, the correct simplified expression is 100^(6), which can be written as 1000000, or "1,000,000".
So, the correct option is: 10,000^15.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we add the exponents of the same base. The Product Rule states that a^m * a^n = a^(m+n).
In this case, we have 1008 * 1007.
To find the answer, we need to determine the sum of the exponents of the base 10.
Since both numbers have a base of 10, we add the exponents together:
8 + 7 = 15
So the correct option that uses the Product Rule of Exponents is 100^15.