To simplify the expression [tex]\(\frac{14 x^4 y^6}{7 x^6 y^3}\)[/tex], follow these steps:
1. Factor the constants:
Simplify the constants in the numerator and the denominator.
[tex]\[
\frac{14}{7} = 2
\][/tex]
2. Handle the [tex]\(x\)[/tex] terms:
Simplify the exponent of [tex]\(x\)[/tex] by subtracting the exponent in the denominator from the exponent in the numerator.
[tex]\[
x^4 \div x^6 = x^{4-6} = x^{-2} = \frac{1}{x^2}
\][/tex]
3. Handle the [tex]\(y\)[/tex] terms:
Simplify the exponent of [tex]\(y\)[/tex] by subtracting the exponent in the denominator from the exponent in the numerator.
[tex]\[
y^6 \div y^3 = y^{6-3} = y^3
\][/tex]
4. Combine all the factors:
Putting all the parts together:
[tex]\[
\frac{14 x^4 y^6}{7 x^6 y^3} = 2 \cdot \frac{y^3}{x^2}
\][/tex]
So the simplified form of the given expression is:
[tex]\[
\frac{2 y^3}{x^2}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{2 \cdot \frac{y^3}{x^2}}
\][/tex]
Thus, the expression equivalent to [tex]\(\frac{14 x^4 y^6}{7 x^6 y^3}\)[/tex] is:
[tex]\[
\boxed{D. \frac{2 y^3}{x^2}}
\][/tex]
