Question

Simplify$\frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}$

Short answer

On simplifying the given expression, we get

$\frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{36}{25}$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Theexpressiongivenis}\\ \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Simplify the numerator and denominator 

$\begin{array}{l}\Rightarrow \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{\left(\frac{3^2}{4^2}\right)}{\left(\frac{5^2}{8^2}\right)}\\ \Rightarrow \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{\left(\frac{9}{16}\right)}{\left(\frac{25}{64}\right)}\end{array}$

Step 3. Simplify the fraction 

$\begin{array}{l}\Rightarrow \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{\left(\frac{9}{16}\right)}{\left(\frac{25}{64}\right)}\\ \Rightarrow \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{9}{16}\times \frac{64}{25}\\ \Rightarrow \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{9}{\cancel{16}}\times \frac{\cancel{16}\times 4}{25}\\ \Rightarrow \frac{{\left(\frac{3}{4}\right)}^2}{{\left(\frac{5}{8}\right)}^2}=\frac{36}{25}\end{array}$