Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10,00015
10056
10015
20015
The correct response is 10015.
The product rule of exponents states that when multiplying two numbers with the same base, you add their exponents. In this case, the base is 10 and the exponents are 1008 and 1007. Therefore, you add 1008 and 1007 to get 2015.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents:
Step 1: Rewrite each base with the same base raised to the sum of the exponents.
The base is 10, and the exponents are 1008 and 1007.
Step 2: Apply the Product Rule of Exponents, which states that when multiplying two numbers with the same base, you add the exponents.
1008⋅1007 = 10^(1008 + 1007)
Step 3: Simplify the exponent.
10^(1008 + 1007) = 10^2015
Therefore, the correct answer is 10,00015.