Calculate (2/3)²: Evaluating the Square of a Fraction

To solve this problem, we'll follow these steps:

• Apply the exponentiation rule to the fraction $\frac{2}{3}$.
• Calculate $2^2$ and $3^2$.
• Form the result as a fraction.
• Compare the result to the provided choices and select the correct one.

Now, let's work through each step:

Step 1: The expression given is $\left(\frac{2}{3}\right)^2$.

Step 2: According to the exponentiation rule, we apply the exponent to both the numerator and the denominator:
$\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2}$.

Step 3: Calculate $2^2$ and $3^2$:
$2^2 = 4$, and $3^2 = 9$.

Step 4: Form the resultant fraction:
Thus, $\frac{2^2}{3^2} = \frac{4}{9}$.

Step 5: Finally, compare this result with the given choices:
Our result $\frac{4}{9}$ matches with choice 2.

Therefore, the solution to the problem is $\frac{4}{9}$.