Question

Which expression is equivalent to the given expression?

Assume the denominator does not equal zero.

$\frac{14x^4{y}^6}{7x^8{y}^2}$

• A. $\frac{2y^4}{x^4}$
• B. $\frac{2y^3}{x^2}$
• C. $7x^4{y}^4$
• D. $2x^2{y}^3$

Answer 1

The correct option is A

$\frac{2y^4}{x^4}$

Explanation for correct option:

Find the equivalent expression for the Equation $\frac{14x^4{y}^6}{7x^8{y}^2}$

Consider the given expression as,

$\frac{14x^4{y}^6}{7x^8{y}^2}$

According to the question,

It is given, to be assume that denominator does not equal zero.

Now by given expression, i.e.

$\frac{14x^4{y}^6}{7x^8{y}^2}$

The greatest common factor(GCF) of expression is $7x^4{y}^2$

Now, divide denominator and numerator by GCF we get,

$$\begin{gathered} \Rightarrow \frac{14x^4{y}^6}{7x^8{y}^2}=\frac{{\displaystyle \frac{14x^4{y}^6}{7x^8{y}^2}}}{{\displaystyle \frac{7x^8{y}^2}{7x^4{y}^2}}} \\ \Rightarrow \frac{14x^4{y}^6}{7x^8{y}^2}=\frac{2y^4}{x^4} \end{gathered}$$

Therefore, the correct answer is option (A) .