Evaluate or simplify each expression without using a calculator. In 1

Verified step by step guidance

1. First, carefully read the problem statement to identify the expression that needs to be evaluated or simplified. Since the problem references Exercises 81–100 but only mentions 'In 1', clarify or locate the exact expression to work on.
2. Once the expression is identified, rewrite it clearly using proper algebraic notation. For example, if the expression involves exponents, roots, or fractions, write it out explicitly.
3. Apply algebraic properties such as the laws of exponents, distributive property, or factoring techniques to simplify the expression step-by-step. For example, use the rule \(a^{m} \times a^{n} = a^{m+n}\) to combine like bases.
4. Continue simplifying by combining like terms, reducing fractions, or rationalizing denominators as needed, ensuring each step follows logically from the previous one.
5. After simplification, verify that the expression is in its simplest form by checking for any further reductions or factorizations possible.

Key Concepts

Order of Operations

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to correctly simplify expressions. It follows the PEMDAS/BODMAS rule: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right). Understanding this ensures accurate evaluation without a calculator.

Simplifying Algebraic Expressions

Simplifying expressions involves combining like terms, applying distributive properties, and reducing expressions to their simplest form. This process helps in making expressions easier to work with and is essential when evaluating expressions manually.

Properties of Exponents

Properties of exponents include rules such as product of powers, power of a power, and quotient of powers, which help simplify expressions involving exponents. Mastery of these properties allows for efficient simplification and evaluation of expressions without a calculator.