Product Rule of Exponents Quick Check
Math 8 Q1 (Pre-Algebra) / Exponent Rules
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
100^56
100^15
10,000^15
200^15
The correct answer is: 100^15.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we need to add the exponents when multiplying the same base.
Let's analyze the given options:
1. 100^56: This option does not use the correct base. The base should be 100, not 1000.
2. 100^15: This option uses the correct base of 100 but does not consider both terms being multiplied.
3. 10,000^15: This option uses the correct base of 10,000 but does not consider both terms being multiplied.
4. 200^15: This option does not use the correct base. The base should be 100, not 200.
None of the given options correctly uses the Product Rule of Exponents to simplify the expression 1008⋅1007.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we need to add the exponents of the common base, which in this case is 10.
The Product Rule of Exponents states that when we multiply two numbers with the same base raised to different exponents, we can add the exponents together. Therefore, the correct answer would have the base (10) raised to the sum of the exponents.
Let's break down the given options:
1. 100^56
This option does not apply the Product Rule of Exponents correctly because it uses 100 as the base instead of 10. The base should be 10, and the exponents should be added, not multiplied.
2. 100^15
Again, this option uses 100 as the base instead of 10. It does not correctly apply the Product Rule of Exponents.
3. 10,000^15
This option correctly applies the Product Rule of Exponents. It uses 10,000 (which is equal to 10^4) as the base, and the exponent is 15. Thus, this option simplifies the expression 1008⋅1007 correctly.
4. 200^15
This option does not correctly apply the Product Rule of Exponents. It uses a base of 200 instead of 10. The base should be 10, and the exponents should be added, not multiplied.
Therefore, the correct answer is 10,000^15.