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Understanding the order of operations is crucial when it comes to simplifying mathematical expressions. It is a set of rules that dictates the sequence in which operations should be carried out to accurately calculate an expression. This sequence is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let’s apply this to the given exercise \( [-(-3)]^{2} \). First, we address the innermost part of the expression, which are the parentheses \( -(-3) \), essentially telling us to resolve this before dealing with the exponentiation. By following PEMDAS, we ensure that all components of the expression are simplified in the correct order, leading to the accurate final answer.

Negative numbers often confuse students, but they follow a simple set of rules that, once understood, make calculations much clearer. In our exercise, we encounter a negative sign before parentheses, which contains another negative number. The rule here is that two negatives make a positive — so \( -(-3) \) becomes \( +3 \).

When simplifying expressions with negative numbers, always remember this key rule. It helps to visualize negative numbers as the opposite direction on a number line — when you 'go negative' twice, you end up back in the positive direction. It's a concept that you'll see time and again in math, so becoming comfortable with how to handle negative numbers is essential.

Exponentiation is the process of raising a number to a power, which signifies how many times to multiply the number by itself. For instance, in the expression \( (3)^{2} \), the number 3 is the base and 2 is the exponent. It instructs us to multiply 3 by itself exactly 2 times, resulting in \( 3*3 = 9 \).

One common mistake is to confuse exponentiation with multiplication — remember that \( 3*2 \) is just adding 3 twice, while \( 3^2 \) is multiplying 3 by itself. Exponentiation can also involve negative numbers and other exponents, which add layers of complexity but are based on this fundamental concept. Understanding how to apply exponentiation within the order of operations is key to simplifying expressions correctly.