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Select the correct answer.

Which expression is equivalent to the given expression? Assume the denominator does not equal zero.

[tex]\[ \frac{12 x^3 y^4}{6 x^3 y^2} \][/tex]

A. [tex]\(2 x^3 y^2\)[/tex]

B. [tex]\(\frac{2}{x^6 y^2}\)[/tex]

C. [tex]\(\frac{2}{z^2 y^2}\)[/tex]

D. [tex]\(2 x^6 y^2\)[/tex]


Sagot :

To simplify the given expression [tex]\(\frac{12 x^3 y^4}{6 x^3 y^2}\)[/tex], we will follow these steps:

1. Separate the coefficients and the variables:
[tex]\[ \frac{12 x^3 y^4}{6 x^3 y^2} = \frac{12}{6} \cdot \frac{x^3}{x^3} \cdot \frac{y^4}{y^2} \][/tex]

2. Simplify the coefficients:
[tex]\[ \frac{12}{6} = 2 \][/tex]

3. Simplify the [tex]\(x\)[/tex]-terms:
[tex]\[ \frac{x^3}{x^3} = 1 \][/tex]
Since the numerator and denominator are the same, they cancel each other out.

4. Simplify the [tex]\(y\)[/tex]-terms:
[tex]\[ \frac{y^4}{y^2} = y^{4-2} = y^2 \][/tex]
When dividing exponents with the same base, you subtract the exponents.

5. Combine all simplified parts:
[tex]\[ 2 \cdot 1 \cdot y^2 = 2y^2 \][/tex]

Thus, the simplified form of the given expression is:

[tex]\[ \frac{12 x^3 y^4}{6 x^3 y^2} = 2y^2 \][/tex]

Hence, the correct answer is:
[tex]\[ \boxed{2y^2} \][/tex]