91Ó°ÊÓ

Simplifying expressions involves reducing an algebraic expression to its simplest form. The goal is to make the expression as compact and clear as possible, which can help in solving equations or understanding its behavior. In the given exercise, initially, we have a complex expression, \( \left(2^{3} + 2^{2}\right)^{2} \). To simplify it, we broke it down into manageable pieces.

• First, we dealt with the exponents individually: \(2^{3} = 8\) and \(2^{2} = 4\).
• Next, these results were added together, giving us \(8 + 4 = 12\).
• Lastly, we squared the sum to get \(12^{2} = 144\).

By following these steps, the complex expression was simplified to a straightforward numerical value. Simplifying helps us see the essence of an expression without unnecessary complexity.

The order of operations is crucial in mathematics to ensure that expressions are simplified correctly and consistently. The rules can be remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
In the exercise at hand, we applied these rules meticulously:

• Start with operations inside the parentheses: evaluate the exponents - \(2^{3}\) and \(2^{2}\).
• Then, perform the addition inside the parentheses: \(8 + 4 = 12\).
• Finally, apply the exponent outside the parentheses: square the sum \(12^{2} = 144\).

This logical sequence ensures that each step correctly builds on the previous one, leading to an accurate simplification of the expression. By following the order of operations, mathematical expressions are reliably evaluated the same way every time.

Algebraic expressions are combinations of numbers, variables, and operations. They form the basis for many algebraic problems. Understanding how to manipulate these expressions is key to solving algebra problems efficiently.

In the exercise, we focused on an expression composed of exponents and basic arithmetic operations. Expressions can be more complex with variables, coefficients, and multiple operations involved. Here, we're concerned with purely numerical values which simplify our task, but even with variables, the same principles apply.

• Identify individual components like terms, coefficients, operations, and their relationships.
• Apply concepts like combining like terms or using distributive property when necessary.
• Simplify step by step, following the order of operations.

This approach to algebraic expressions, whether they include symbols or not, prepares us for more complex algebraic equation-solving tasks. Mastery of simple expressions lays the groundwork for handling complex ones effectively.