Discover a world of knowledge and get your questions answered at IDNLearn.com. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.

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]
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.