Textbook Question
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x2-6x+3, for x=7
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 7
Evaluate each exponential expression in Exercises 1–22. (−3)0
Verified step by step guidance1
Recall the zero exponent rule, which states that for any nonzero base \(a\), \(a^0 = 1\).
Identify the base in the expression \((\-3)^0\). Here, the base is \(-3\).
Since \(-3\) is a nonzero number, apply the zero exponent rule: \((\-3)^0 = 1\).
Understand that the parentheses indicate the entire number \(-3\) is raised to the zero power, not just the 3.
Conclude that the value of \((\-3)^0\) is 1, based on the zero exponent rule.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Powers
Exponents indicate how many times a base number is multiplied by itself. For example, in a^n, 'a' is the base and 'n' is the exponent, meaning multiply 'a' by itself 'n' times. Understanding this helps evaluate expressions like (−3)^0.
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Zero Exponent Rule
Any nonzero base raised to the zero power equals 1. This means that for any number 'a' ≠ 0, a^0 = 1. This rule applies regardless of whether the base is positive or negative, so (−3)^0 = 1.
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Order of Operations with Exponents
When evaluating expressions with exponents, apply the exponent before other operations like multiplication or addition. Parentheses indicate that the exponent applies to the entire base, so (−3)^0 means the whole number −3 is raised to the zero power.
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Related Practice
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In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x^2+3x, for x=8
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In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x2−6x+9)
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