Question

Match the products of rational expressions with their simplest forms.

Answer 1

Lets simplify each one of the rational expressions using the product rule of exponents: $a^n*a^m=a^{n+m}$ and the quotient rule of exponents: $\frac{a^n}{a^m} =a^{n-m}$.

1.  $\frac{-3x^2}{2y^2} * \frac{y^2}{9x} =- \frac{x}{6} = \frac{-1}{6} x$

2. $\frac{5y^2}{10x^2} * \frac{4x^2}{y} =2y$

3. $\frac{-9y^2}{5x} * \frac{-10x^2}{3y} =6xy$

4. $\frac{14x^2}{5y} * \frac{-10y}{7x} =-4x$

We can conclude that you should pair the rational expressions with their simplest form as follows:
$6xy-----\ \textgreater \ \frac{-9y^2}{5x} * \frac{-10x^2}{3y}$
$\frac{-1}{6} x-----\ \textgreater \ \frac{-3x^2}{2y^2} * \frac{y^2}{9x}$
$-4x-----\ \textgreater \ \frac{14x^2}{5y} * \frac{-10y}{7x}$
$2y-----\ \textgreater \ \frac{5y^2}{10x^2} * \frac{4x^2}{y}$