Question

Simplify the expression $\frac{{\left(-2r{s}^2\right)}^2}{12r^2{s}^3}$.

Short answer

The simplified value of expression is $\frac{s}{3}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $\frac{{\left(-2r{s}^2\right)}^2}{12r^2{s}^3}$.

Step 2. Simplify the expression.

The given expression $\frac{{\left(-2r{s}^2\right)}^2}{12r^2{s}^3}$is simplified as:

$\begin{array}{l}\frac{{\left(-2r{s}^2\right)}^2}{12r^2{s}^3}=\frac{4r^2{s}^4}{12r^2{s}^3}\\ =\frac{r^2{s}^4}{3r^2{s}^3}\\ =\frac{r^{2-2}{s}^{4-3}}{3}\\ =\frac{s}{3}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{s}{3}$.