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Evaluating expressions is a fundamental skill in mathematics, especially in prealgebra and algebra contexts. It involves substituting the given values of variables into an expression and then simplifying the expression to find its value. In our example, we have the expression \(b^0 - 10\), where \(b = 4\).
To evaluate, we start by applying known mathematical rules, such as the zero exponent rule. This rule tells us that any non-zero number raised to the power of zero equals one. So, for \(b = 4\), we have:

• Substitute \(b = 4\) into \(b^0\), resulting in \(4^0 = 1\).
• Replace \(b^0\) with 1 in the expression, leading to \(1 - 10\).

Now, we perform the subtraction to simplify the expression further. Evaluating expressions in this manner is a step-by-step process that helps to clarify how variables interact with constants within mathematical operations.

Performing operations with integers, such as addition, subtraction, multiplication, and division, is a key aspect of working with algebraic expressions. In our example expression \(b^0 - 10 = 1 - 10\), we deal with subtraction of integers.
Here’s how integer subtraction works in our case:

• The expression simplifies to \(1 - 10\).
• Since both numbers are integers, we consider their signs; 1 is positive, and 10 is positive, but we are subtracting it.
• Subtracting these gives \(-9\); essentially, we have moved 9 steps to the left on a number line starting from 1.

This clear method helps see how the rules of integer operations apply practically. By understanding integer operations, you can handle more complex expressions and equations efficiently.

Prealgebra lays the groundwork for algebra, introducing key concepts such as evaluating expressions and understanding the properties of numbers. In this specific problem, we apply the zero exponent rule, a crucial concept in prealgebra, which helps us simplify expressions.
These are the key prealgebra concepts involved in our problem:

• Zero Exponent Rule: Any non-zero number to the zero power equals one.
• Operations with integers: Understanding how to add and subtract integers is crucial.

By mastering these concepts, students build the necessary skills to transition smoothly into more advanced algebraic thinking. This foundational understanding then supports further math learning involving complex polynomial and rational expressions.