To solve the problem of dividing [tex]\(-12x^8y^8\)[/tex] by [tex]\(3x^4y^2\)[/tex], follow these steps:
1. Divide the coefficients:
The coefficients are [tex]\(-12\)[/tex] and [tex]\(3\)[/tex]. When you divide [tex]\(-12\)[/tex] by [tex]\(3\)[/tex], the result is:
[tex]\[
\frac{-12}{3} = -4
\][/tex]
2. Divide the variables with exponents:
For [tex]\(x\)[/tex], the exponents are [tex]\(8\)[/tex] and [tex]\(4\)[/tex]. When you divide [tex]\(x^8\)[/tex] by [tex]\(x^4\)[/tex], you subtract the exponents:
[tex]\[
x^{8-4} = x^4
\][/tex]
For [tex]\(y\)[/tex], the exponents are [tex]\(8\)[/tex] and [tex]\(2\)[/tex]. When you divide [tex]\(y^8\)[/tex] by [tex]\(y^2\)[/tex], you subtract the exponents:
[tex]\[
y^{8-2} = y^6
\][/tex]
3. Combine the results:
Now, combine the results from the coefficients and the variables:
[tex]\[
-4 \cdot x^4 \cdot y^6
\][/tex]
Thus, the result of dividing [tex]\(-12x^8y^8\)[/tex] by [tex]\(3x^4y^2\)[/tex] is:
[tex]\[
-4x^4y^6
\][/tex]
Therefore, the correct answer is option D:
[tex]\[
\boxed{-4 x^4 y^6}
\][/tex]
