Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007 ?(1 point)
The Product Rule of Exponents states that for numbers a and b, and any positive integers m and n, a^m ⋅ b^n = a^(m+n).
Therefore, to simplify the expression 1008⋅1007 using the Product Rule of Exponents, we can rewrite it as (10^2 * 100) ⋅ (10^2 * 100 + 7), which can be further simplified as (10^4 * 100 * 107) = 10^4 * 100, which is equal to 100*100 = 10000.
So the correct answer is 10000.
are you sure?
I apologize for the confusion in my previous response. I made an error in applying the Product Rule of Exponents.
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we can write it as 10^3 ⋅ 2^4 ⋅ 503, since 1008 can be factored into 10^3 ⋅ 2^4 ⋅ 7^1.
Therefore, the correct answer is 10^3 ⋅ 2^4 ⋅ 503.
Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8⋅100^7 ?(1 point)
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we can add the exponents of the same base, which in this case is 10.
The Product Rule of Exponents states that for any positive integers a, b, and c: ab⋅ac = ab+c.
In this case, we have 1008⋅1007 = (10^3 ⋅ 10^0)⋅(10^3 ⋅ 10^(-1)).
Because we have the same base, we can apply the Product Rule and add the exponents: 10^(3+0)⋅10^(3+(-1)) = 10^3 ⋅ 10^2.
Therefore, the correct simplification of 1008⋅1007 using the Product Rule of Exponents is 10^3 ⋅ 10^2.
To correctly use the Product Rule of Exponents to simplify the expression 1008⋅1007, we need to add the exponents of the common base, which is 10.
The Product Rule of Exponents states that for any non-zero real number a and any integers m and n:
a^m ⋅ a^n = a^(m + n)
So, the correct application of the Product Rule for this expression would be:
1008⋅1007 = 10^3 ⋅ 10^2 = 10^(3+2) = 10^5
Therefore, the correct way to simplify the expression using the Product Rule of Exponents is 10^5.