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Exponents are a shorthand way of expressing repeated multiplication of the same number. They consist of a base and an exponent, which is written as a superscript. The base is the number that is being multiplied, while the exponent tells us how many times the base is multiplied by itself.
For example, in the expression \((3)^2\), 3 is the base and 2 is the exponent. This means we multiply 3 by itself: \(3 \times 3 = 9\).
This concept comes into play significantly when simplifying mathematical expressions involving exponents. Evaluating exponents is typically one of the first steps when simplifying, as it helps reduce the complexity of the problem early on.

Parentheses are crucial in mathematics as they dictate the order in which operations are performed. The standard order of operations can be remembered using the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
When we see an expression with parentheses, such as \((5-2)\), we must solve this part first before doing anything outside the parentheses. This is because the operations within the parentheses could alter the values that affect subsequent operations.
In the expression \(-2-(5-2)^2\), the subtraction inside the parentheses is handled first, changing the expression to \(-2-(3)^2\) before evaluating the exponent or other operations outside the parentheses. Ignoring the parentheses would lead to incorrect calculations.

Subtraction, in its simplest form, is taking one number away from another. It is one of the primary operations in math and is usually done after evaluating exponents and other more complex operations in an expression.
In the given example, after evaluating the exponent inside the parentheses \((5-2)^2 = 9\), we perform the subtraction:\[-2 - 9 = -11\].
This step involves combining the negative sign with 9, which can sometimes be tricky for learners. This happens because subtracting a positive number like 9 from a negative number such as -2 essentially means moving further into the negative side of the number line. The result in this case is what's known as an additive inverse, leading to the final answer of -11.