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In math, evaluating expressions means finding the value of mathematical expressions by following the order of operations and substituting given values. This is a core skill needed in algebra and beyond. To evaluate an expression, you first need a clear understanding of its components. For example, if you have expressions like \[y^{-1}\], you'll need to break it down into its parts. Make sure you understand any variables, constants, and operations included.

Next, you perform the operations step-by-step, following the mathematical rules or operations. These often include addition, subtraction, multiplication, division, powers, and roots.

By evaluating expressions, you practice solving problems and deepen your knowledge of mathematical concepts.

Substitution is a fundamental technique in algebra used to simplify expressions. It involves replacing variables with their given values. This concept is crucial for solving equations and understanding functions. In our exercise, we were given that \(y = 5\).

To substitute, you simply replace the variable with the given value wherever it appears in the expression. So, if we have an expression \[y^{-1}\], we replace \(y\) with 5 to get \(5^{-1}\). Substitution makes complex expressions more manageable and is widely used in higher mathematics to solve complicated problems.

Negative exponents transform numbers in interesting ways, often making large numbers small and small numbers large. For any non-zero number \(a\), the expression \(a^{-n}\) equals \[\frac{1}{a^n}\].

Consider our exercise with \(y = 5\) and the expression \[y^{-1}\]. A negative exponent indicates a reciprocal. So, \(y^{-1} = 5^{-1}\), which means \[\frac{1}{5}\].
Recognizing how to work with negative exponents is vital in algebra and calculus. It helps you switch between different forms of expressions and solve a broad range of mathematical problems more effectively.