Given the equation $a^2 = 16$, to find the possible values of $a$, we solve for $a$ by taking the square root of both sides.

$a = \pm \sqrt{16}$

Since the square root of 16 can be both positive and negative:

$a = \pm 4$

So, the possible values of $a$ are:

$a = 4 \quad \text{or} \quad a = -4$

Would you like more details on solving equations like this, or do you have any questions? Here are some related questions:

1. How would you solve $a^2 = 25$?
2. What is the square root of a negative number, and how is it related to complex numbers?
3. How can we solve quadratic equations using the square root method?
4. What are the differences between solving equations with even and odd powers?
5. What happens if we solve $a^2 = 0$?

Tip: When solving for $a$ in equations like $a^2 = k$, remember to check for both the positive and negative square roots.