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Exponentiation refers to the mathematical operation where a number (the base) is multiplied by itself a specific number of times (the exponent). For example, in the expression \(5^2\), the base is 5, and the exponent is 2. This means you multiply 5 by itself, resulting in 25. It's important to note that exponentiation is performed before any addition or subtraction in an expression, according to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
In our exercise, \(-5^2+7\), the exponentiation step involves only the positive part of the base, so \(5^2 = 25\). The negative sign is separate and applied after this calculation.

Negative numbers are numbers less than zero, and they are represented with a minus sign (-). They are used to represent quantities that are less than zero, such as debts or temperatures below freezing. In our exercise, after calculating the exponentiation, we need to apply the negative sign:
Step 1: Calculate \(5^2 = 25\)
Step 2: Apply the negative sign, resulting in \(-25\).
This step is crucial as applying the negative sign afterward can sometimes be confusing. It helps to remember that exponentiation comes first, followed by the application of the negative sign, if present.

Addition is one of the basic operations in arithmetic where two or more numbers are combined to get their total. In the context of our exercise, after performing the exponentiation and applying the negative sign, we need to add the remaining number to the result.
Step 3: Adding 7 to the result of \(-25\):
\(-25 + 7\)
is done by combining -25 and 7. This essentially means moving 7 units up from -25 on the number line. Performing this operation gives us \(-18\).
Always follow the order of operations, ensuring all exponentiations and sign applications are done before performing any addition or subtraction.