To simplify the expression [tex]\(\frac{12 z^9 y^4}{6 z^8 y^2}\)[/tex], we need to break it down into simpler steps.
1. Simplify the coefficients:
[tex]\[
\frac{12}{6} = 2
\][/tex]
2. Simplify the [tex]\(z\)[/tex] terms using the laws of exponents:
[tex]\[
\frac{z^9}{z^8} = z^{9-8} = z^1 = z
\][/tex]
3. Simplify the [tex]\(y\)[/tex] terms using the laws of exponents:
[tex]\[
\frac{y^4}{y^2} = y^{4-2} = y^2
\][/tex]
Combining these results, the simplified form of the expression is:
[tex]\[
2 z y^2
\][/tex]
Therefore, the correct answer is:
D. [tex]\(2 z y^2\)[/tex]
