To find an expression equivalent to [tex]\(\frac{12 x^2 y^4}{6 x^1 y^2}\)[/tex], we need to simplify the fraction step-by-step. Let's start by breaking down the numerator and the denominator:
[tex]\[
\text{Numerator} = 12x^2y^4
\][/tex]
[tex]\[
\text{Denominator} = 6xy^2
\][/tex]
We can simplify the numerical coefficients first:
[tex]\[
\frac{12}{6} = 2
\][/tex]
Next, simplify the [tex]\(x\)[/tex] terms. When dividing exponential terms with the same base, subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
x^2/x = x^{2-1} = x^1 = x
\][/tex]
Now, simplify the [tex]\(y\)[/tex] terms using the same rule for exponents:
[tex]\[
y^4/y^2 = y^{4-2} = y^2
\][/tex]
Putting these simplified components together, we get:
[tex]\[
2 \cdot x \cdot y^2 = 2xy^2
\][/tex]
Therefore, the expression [tex]\(\frac{12 x^2 y^4}{6 x y^2}\)[/tex] simplifies to:
[tex]\[
2xy^2
\][/tex]
Hence, the correct answer is:
A. [tex]\( 2 x y^2 \)[/tex]
