Question

$\begin{array}{l}\text{Inthefollowingexercise,evaluate.}\\ 2x^2{y}^3\text{When}\\ x=-\frac{2}{3}\text{and}y=-\frac{1}{2}\end{array}$

Short answer

$\text{Theresultonevaluatingtheexpressionis-}\frac{1}{9}\text{.}$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionis}\\ 2x^2{y}^3\\ \text{Also,}\\ x=-\frac{2}{3}\text{and}y=-\frac{1}{2}\\ \text{Wewillevaluatetheexpressionforgivenvaluesof}x\text{and}y.\end{array}$

Step 2. Substitute the value of x and y in the given expression

$\begin{array}{l}\text{At}x=-\frac{2}{3}\text{and}y=-\frac{1}{2},\text{Wehave}\\ \Rightarrow 2{\left(-\frac{2}{3}\right)}^2{\left(-\frac{1}{2}\right)}^3\\ =2\left(\frac{4}{9}\right)\left(-\frac{1}{8}\right)\\ =\frac{2\times 4\times \left(-1\right)}{9\times 8}\\ =-\frac{\cancel{8}}{9\times \cancel{8}}\\ =-\frac{1}{9}\end{array}$