To solve the problem of simplifying the expression [tex]\(\frac{12 x^9 y^4}{6 x^3 y^2}\)[/tex], let's follow a step-by-step approach.
### Step 1: Simplify the Coefficients
First, simplify the numerical part of the fraction:
[tex]\[
\frac{12}{6} = 2
\][/tex]
### Step 2: Simplify the [tex]\(x\)[/tex]-terms
Next, simplify the exponent of [tex]\(x\)[/tex]:
[tex]\[
\frac{x^9}{x^3} = x^{9-3} = x^6
\][/tex]
### Step 3: Simplify the [tex]\(y\)[/tex]-terms
Now, simplify the exponent of [tex]\(y\)[/tex]:
[tex]\[
\frac{y^4}{y^2} = y^{4-2} = y^2
\][/tex]
### Step 4: Combine the Simplified Parts
Combining the simplified numerical, [tex]\(x\)[/tex]-terms, and [tex]\(y\)[/tex]-terms:
[tex]\[
2 \cdot x^6 \cdot y^2 = 2x^6y^2
\][/tex]
### Conclusion
The simplified expression [tex]\(\frac{12 x^9 y^4}{6 x^3 y^2}\)[/tex] is equivalent to [tex]\(2 x^6 y^2\)[/tex].
Thus, the correct answer is:
D. [tex]\(2 x^6 y^2\)[/tex]
