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Algebraic expressions are a fundamental part of algebra. They consist of numbers, variables, and operations like addition or multiplication. Think of them as "math sentences" that describe a calculation. In this problem, the function \(f(x) = 2(9^x)\) is an algebraic expression. It combines constants, a base, and an exponent. The expression \(2-a\) is another example.When working with algebraic expressions, it's crucial to substitute correctly. This means replacing variables with specific values or other expressions. In our exercise, we started by replacing \(x\) with \(2-a\). This step transforms the function into a new expression: \(f(2-a) = 2(9^{2-a})\).Understanding how to manipulate algebraic expressions helps solve equations and perform other algebraic tasks. Always remember to simplify expressions by combining like terms or using mathematical rules.

Exponent rules simplify calculations involving powers. They describe how to handle expressions with exponents efficiently. One of the key exponent rules is \(a^{m+n} = a^m  a^n\). In our exercise, the expression \(9^{2-a}\) is simplified using such rules.The rule we used here is about multiplying terms with the same base. We start with \(9^{2-a}\) and use the property that exponents subtract when dividing: \(9^{2-a} = 9^2  9^{-a}\). Breaking it down results in a simpler expression: \(81  9^{-a}\), because \(9^2\) equals 81.Using exponent rules allows for a clearer outcome without complicating the process. This way, you avoid errors and have a logically organized expression. Explore more rules like \((ab)^n = a^n  b^n\) or \((a^n)^m = a^{nm}\) to further enhance your understanding.

Function evaluation is determining the output of a function for a specific input. It involves substituting the input value into the function equation. In our example, we were given a function \(f(x) = 2(9^x)\) and needed to find \(f(2-a)\).To evaluate the function:

• Substitute \(2-a\) in place of \(x\) in the equation.
• Perform any necessary algebraic simplifications, like using exponent rules.
• Simplify the expression to get the result, which is \(162  9^{-a}\).

Function evaluation is a practical skill used in many mathematical and real-world applications. You may use it to find specific points on a graph or analyze how changes in variables affect outcomes. With consistent practice, you're sure to become proficient at evaluating functions effectively.