Let's simplify the given expression step-by-step:
Given expression: [tex]\(\frac{12 x^2 y^4}{6 x^2 y^3}\)[/tex]
1. Simplify the coefficients:
- The coefficients in the numerator and denominator are 12 and 6, respectively.
- Simplify the coefficients: [tex]\(\frac{12}{6} = 2\)[/tex].
2. Simplify the powers of [tex]\(x\)[/tex]:
- The power of [tex]\(x\)[/tex] in the numerator is [tex]\(x^2\)[/tex].
- The power of [tex]\(x\)[/tex] in the denominator is also [tex]\(x^2\)[/tex].
- Simplify the powers of [tex]\(x\)[/tex]: [tex]\(\frac{x^2}{x^2} = x^{2-2} = x^0 = 1\)[/tex].
3. Simplify the powers of [tex]\(y\)[/tex]:
- The power of [tex]\(y\)[/tex] in the numerator is [tex]\(y^4\)[/tex].
- The power of [tex]\(y\)[/tex] in the denominator is [tex]\(y^3\)[/tex].
- Simplify the powers of [tex]\(y\)[/tex]: [tex]\(\frac{y^4}{y^3} = y^{4-3} = y\)[/tex].
Combining these simplified terms, we get:
[tex]\[ 2 \cdot 1 \cdot y = 2y \][/tex]
Therefore, the simplified expression is [tex]\(2y\)[/tex].
The correct answer is none of the options provided, hence there is a mistake in the choices of options.
