Question

How to evaluate the power ${\left(\frac{2}{3}\right)}^2$?

Answer 1

Evaluate the given expression

Given, ${\left(\frac{2}{3}\right)}^2$,

To evaluate ${\left(\frac{2}{3}\right)}^2$, distribute the power to numerator and denominator separately and solve as shown below.

$\begin{array}{rcl}& \Rightarrow & {\left(\frac{2}{3}\right)}^2=\frac{2^2}{3^2}\end{array}$

$\begin{array}{rcl}& \Rightarrow & {\left(\frac{2}{3}\right)}^2=\frac{4}{9}[\because 2^2=2\times 2,3^2=3\times 3]\end{array}$

Therefore, ${\left(\frac{2}{3}\right)}^2$$=\frac{4}{9}$.