Question

Evaluate each expression.

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

Short answer

The required evaluated value is represented by$\frac{\mathbf{4}}{\mathbf{9}}$.

Step-by-step solution

Step 1. Determine the exponent of provided expression as it will represent the count of its factors.

The provided expression contains$\frac{2}{3}$ as the base and 2 as its exponent.

Step 2. Use the obtained base and exponent to determine the required evaluated value.

For numerator, perform multiplication of 2 by itself 2 times and for denominator, perform multiplication of 3 by itself 2 times to get the required value.

$\begin{array}{c}\frac{2^2}{3^2}=\frac{2\cdot 2}{3\cdot 3}\\ =\frac{4}{9}\end{array}$

Step 3. Write the conclusion. 

The obtained value is in simplified form which means that$\frac{4}{9}$ is the required evaluated value.