To simplify the expression [tex]\(\frac{12 x^9 y^4}{6 x^9 y^3}\)[/tex], follow these steps:
1. Simplify the Constants:
[tex]\[
\frac{12}{6} = 2
\][/tex]
2. Simplify the [tex]\(x\)[/tex] Terms:
Since [tex]\(x^9\)[/tex] appears in both the numerator and the denominator, we can write:
[tex]\[
\frac{x^9}{x^9} = x^{9-9} = x^0 = 1
\][/tex]
3. Simplify the [tex]\(y\)[/tex] Terms:
Since [tex]\(y^4\)[/tex] is in the numerator and [tex]\(y^3\)[/tex] is in the denominator, we subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
\frac{y^4}{y^3} = y^{4-3} = y^1 = y
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
2 \cdot 1 \cdot y = 2y
\][/tex]
So, the equivalent expression is:
[tex]\[
2y
\][/tex]
Now, let's compare this with the given options:
A. [tex]\(2 x^3 y^2\)[/tex]
B. [tex]\(\frac{2}{x^8 y^2}\)[/tex]
C. [tex]\(\frac{2}{x^2 y^2}\)[/tex]
D. [tex]\(2 x^6 y^2\)[/tex]
None of the options exactly match our simplified expression [tex]\(2y\)[/tex]. There seems to be a mistake in the provided answer choices since the correct simplified form, based on my calculations, is indeed [tex]\(2y\)[/tex]. If the correct answer were present, it would be labeled as [tex]\(2y\)[/tex].
