Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Elementary Algebra
Topic: Exponents and Polynomials
Subtopic: Negative Exponents

Overview

Throughout the course we have been working with positive exponents, but in this lesson we formalize the processes and rules. We also add to our repertoire negative exponents (like 2-4 and x-3) and powers of zero (like 30 and -y0). Negative powers mean to take a reciprocal (flip), so for example: x-3 means 1/x3, (2x)-4=1/(2x)4=1/(16x4), 2x-4=2/x4, and (2/x)-4=(x/2)4=x4/16.

Caution: Notice how important the parentheses are? They indicate exactly what is to the power and what isn't. Careful!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 6.1.1 Understand the effect of a zero or negative power on a number or variable
• 6.1.2 Simplify expressions containing integer exponents (positive, negative, and zero)
• 6.1.3 Use the rules of exponents (product rule, power rule, and quotient rule) accurately

Terminology

Terms you should be able to define: zero power, negative power, product rule of exponents, power rules of exponents, quotient rule of exponents (memorize all three rules!)