To determine the result of dividing [tex]\(-12 x^8 y^8\)[/tex] by [tex]\(3 x^4 y^2\)[/tex], let's break it down step by step:
1. Divide the coefficients:
The coefficient of [tex]\(-12 x^8 y^8\)[/tex] is [tex]\(-12\)[/tex] and the coefficient of [tex]\(3 x^4 y^2\)[/tex] is [tex]\(3\)[/tex].
Dividing [tex]\(-12\)[/tex] by [tex]\(3\)[/tex]:
[tex]\[
\frac{-12}{3} = -4
\][/tex]
2. Divide the variables with exponents:
- For the [tex]\(x\)[/tex] terms:
[tex]\[
x^8 \div x^4 = x^{8-4} = x^4
\][/tex]
- For the [tex]\(y\)[/tex] terms:
[tex]\[
y^8 \div y^2 = y^{8-2} = y^6
\][/tex]
Putting it all together, the result of dividing [tex]\(-12 x^8 y^8\)[/tex] by [tex]\(3 x^4 y^2\)[/tex] is:
[tex]\[
-4 x^4 y^6
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{-4 x^4 y^6}
\][/tex]
So, the best answer is D. [tex]\( -4 x^4 y^6 \)[/tex].
