Final answer:
After multiplying the coefficients and adding the exponents, the expression 6a^6b × 2ab simplifies to 12a^7b^2. None of the provided options match this simplified expression correctly. Therefore, the correct answer, 12a^7b^2, is not listed among the options.
The correct answer is D.
Step-by-step explanation:
To simplify the expression 6a^6b × 2ab completely, we need to apply the rules of exponents and multiplication. We'll multiply the coefficients (6 and 2) and add the exponents of like bases.
First, multiply the coefficients:
6 × 2 = 12
Next, apply the rule of exponents, which states that when multiplying like bases, you add the exponents:
a^6 × a = a^(6+1) = a^7
Finally, do the same with the b variables:
b × b = b^(1+1) = b^2
Putting it all together, we get:
12 × a^7 × b^2, which is choice D) 12a^7b^2.
However, none of the provided answer options correctly matches the simplified expression. The correct answer is 12a^7b^2, but this is not listed among the options A) 8a^6b, B) 12a^6b, C) 8a^6.