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When you look at an expression like \((-5)^{1}\), the first thing you need to identify are the base and the exponent. Understanding these two components is crucial for evaluating expressions with exponents.
The **base** is the number that is being multiplied. In this scenario, the base is \(-5\). The base is essentially the main number that represents the quantity being repeatedly multiplied by itself.
The **exponent** indicates how many times the base is used as a factor in the multiplication. Here, the exponent is \(1\). This tells you that the base, \(-5\), is used only once. When an exponent is \(1\), it means you just have the base itself; no multiplication is necessary.
Understanding the roles of the base and exponent will help clarify how expressions are constructed and evaluated.

Exponent rules are guidelines that simplify the process of working with powers and exponents. These rules make it easier to handle various calculations and are fundamental in algebra.
One of the simplest and most commonly used rules is that any number raised to the power of \(1\) is the number itself. This is known as the "Identity Property of Exponents." For example, in \((-5)^{1}\), using this rule, we know instantly that the result is \(-5\). This is because multiplying \(-5\) by itself only once doesn't change its value.
Such rules exist to simplify mathematical expressions and make calculations faster and more efficient. Familiarizing yourself with them can help you tackle more complex expressions with ease. Always start by identifying which exponent rule applies to your expression before evaluating it.

Evaluating expressions is a crucial skill in mathematics that involves finding the value of an expression. With exponents, evaluation can seem tricky at first, but it becomes simple when you apply the right rules and understand the structure.
To evaluate \((-5)^{1}\), you start by identifying the base and exponent, as mentioned earlier. You then apply the relevant exponent rule—in this case, the rule that any number raised to the power of \(1\) remains the same.
After applying the rule to \((-5)^{1}\), you get \(-5\). Since there are no further operations to perform, you have successfully evaluated the expression.
Practicing evaluation with different expressions, especially those involving higher exponents or multiple terms, builds a strong mathematical foundation. Always remember: understanding the base, identifying the exponent, applying the correct rule, and simplifying are your keys to success.