Question

$\begin{array}{l}\text{Inthefollowingexercise,evaluate.}\\ 8u^2{v}^3\text{When}\\ u=-\frac{3}{4}\text{and}v=-\frac{1}{2}\end{array}$

Short answer

$\text{Theresultofevaluatingtheexpressionis}-\frac{9}{16}.$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenexpressionis}\\ 8u^2{v}^3\\ \text{Also,}\\ u=-\frac{3}{4}\text{and}v=-\frac{1}{2}\\ \text{Wewillevaluatetheexpressionforgivenvaluesof}u\text{and}v\end{array}$

Step 2. Substitute the value of u and v in the given expression

$\begin{array}{l}\text{At}u=-\frac{3}{4}\text{and}v=-\frac{1}{2},\text{Wehave}\\ \Rightarrow 8{\left(-\frac{3}{4}\right)}^2{\left(-\frac{1}{2}\right)}^3\\ =8\left(\frac{9}{16}\right)\left(-\frac{1}{8}\right)\\ =\frac{8\times 9\times \left(-1\right)}{16\times 8}\\ =-\frac{\cancel{8}\times 9}{16\times \cancel{8}}\\ =-\frac{9}{16}\end{array}$