Question

In the following exercises, simplify.

$-\frac{270x^3}{198y^2}$

Short answer

The simplest form of$-\frac{270x^3}{198y^2}$is$-\frac{15x^3}{11y^2}.$

Step-by-step solution

Step 1. Given information

The fraction is$-\frac{270x^3}{198y^2}$.

Step 2. Simplify

$$\begin{gathered} -\frac{270x^3}{198y^2}=-\frac{2\times 3\times 3\times 15\times x^3}{2\times 3\times 3\times 11\times y^2}\text{Factorizethenumeratoranddenominator} \\ =-\frac{\left(2\times 3\times 3\right)\times 15\times x^3}{\left(2\times 3\times 3\right)\times 11\times y^2}\text{Groupcommonfactorsof}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denominator} \\ =-\frac{15x^3}{11y^2}\text{Cancelcommonfactorsof}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denominator} \end{gathered}$$

Hence,$-\frac{270x^3}{198y^2}=-\frac{15x^3}{11y^2}$