Simplify (a/3)²: Squaring a Specific Fraction Expression

Insert the corresponding expression:

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

We need to rewrite the expression $\left(\frac{a}{3}\right)^2$ using the rule of exponents for fractions. This rule states that if you have a fraction $\left(\frac{m}{n}\right)$ and you raise it to a power $k$, it is equivalent to raising both the numerator and the denominator to the power $k$. Therefore, we have:

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

Here, $a^2$ is the numerator and $3^2$ is the denominator. The expression simplifies to:

$\frac{a^2}{9}$

Based on the provided choices, the correct answer is:

Choice 1: $\frac{a^2}{3^2}$

Therefore, the solution to the given problem is $\frac{a^2}{3^2}$.