11. What is the result if you divide [tex]-12x^8y^8[/tex] by [tex]3x^4y^2[/tex]?

A. [tex]-4x^2y^4[/tex]
B. [tex]4x^2y^4[/tex]
C. [tex]4x^4y^6[/tex]
D. [tex]-4x^4y^6[/tex]



Answer :

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]