In Exercises 4–6, evaluate each algebraic expression for the given value or values of the variable. 6+2(x-8)³, for x=11

Verified step by step guidance

1. Substitute the given value of x into the expression: replace x with 11 in the expression 6 + 2(x - 8)^3.
2. Simplify the expression inside the parentheses: calculate (11 - 8).
3. Raise the result from the previous step to the power of 3: compute (3)^3.
4. Multiply the result of the exponentiation by 2: calculate 2 times the result from the previous step.
5. Add the result from the multiplication to 6: compute 6 plus the result from the previous step.

Key Concepts

Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It does not have an equality sign and can represent a value depending on the values assigned to its variables. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which different operations should be performed in a mathematical expression. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept ensures that expressions are evaluated correctly and consistently.

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent, where the base is multiplied by itself as many times as indicated by the exponent. In the expression (x-8)³, the exponent 3 signifies that (x-8) is multiplied by itself three times, which is crucial for accurately evaluating the expression.