Question

Simplify$\frac{2^3+4^2}{{\left(\frac{2}{3}\right)}^2}$

Short answer

On simplifying the given expression, we get

$\frac{2^3+4^2}{{\left(\frac{2}{3}\right)}^2}=54$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Theexpressiongivenis}\\ \frac{2^3+4^2}{{\left(\frac{2}{3}\right)}^2}\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Simplify the numerator and denominator 

$\begin{array}{l}\Rightarrow \frac{2^3+4^2}{{\left(\frac{2}{3}\right)}^2}=\frac{8+16}{\left(\frac{2^2}{3^2}\right)}\\ =\frac{24}{\left(\frac{4}{9}\right)}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow \frac{2^3+4^2}{{\left(\frac{2}{3}\right)}^2}=\frac{24}{\left(\frac{4}{9}\right)}\\ =\frac{24\times 9}{4}\\ =\frac{\cancel{4}\times 6\times 9}{\cancel{4}}\\ =54\end{array}$