Systems of Equations
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Raising an Exponential Expression to a Power
Horizontal Line Test
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Mixed Numbers and Improper Fractions
Solving Quadratic Equations by Completing the Square
Solving Exponential Equations
Adding and Subtracting Polynomials
Factorizing simple expressions
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Simplified Form of a Square Root
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Multiplication Property of Radicals
Determining if a Function has an Inverse
Scientific Notation
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Factoring Polynomials by Grouping
Solving Linear Systems of Equations
Exponential Functions
Factoring Trinomials by Grouping
The Slope of a Line
Simplifying Complex Fractions That Contain Addition or Subtraction
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Solving Right Triangles
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Domain and Range of a Function
Multiplying Polynomials
Slope of a Line
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Percent of Change
Equations Involving Fractions or Decimals
Simplifying Expressions Containing only Monomials
Solving Inequalities
Quadratic Equations with Imaginary Solutions
Reducing Fractions to Lowest Terms
Prime and Composite Numbers
Dividing with Exponents
Dividing Rational Expressions
Equivalent Fractions
Graphing Quadratic Functions
Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
Factoring Polynomials Completely
Using Slopes to Graph Lines
Fractions, Decimals and Percents
Solving Systems of Equations by Substitution
Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Adding and Subtracting Polynomials
The Rectangular Coordinate System
Polar Form of a Complex Number
Exponents and Order of Operations
Graphing Horizontal and Vertical Lines
Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
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Dividing with Exponents

⇒ Definition of Negative Exponent

Note: They are reciprocals.

Example 1:

a) Notice that a negative exponent does not affect the sign of the number.

b) → Odd or Even exponents determine the sign.


⇒ Division of powers with positive exponents:

Notice that 7 − 3 = 4.

or Subtract the smaller exponent from the larger exponent and put the resulting "power" in the "place" of the larger "power".

Put a 1 in the numerator if the larger "power" is in the denominator.


Example 2:

→ Notice that 7 – 3 = 7 + (-3) = + 4


⇒ Operation of powers with negative exponents: Two methods:

Method 1: Follow the rule above carefully keeping the negative exponents in parens:

Example 3:

a) Since 7 > -2 work in the numerator:

b) Since 2 > -8 work in the denominator:

c) Since - 4 > - 9 work in the denominator:

Method 2: To multiply or divide with "most" negative exponents, multiply both the numerator and the denominator by the "reciprocal with positive power" and "neutralize the negative".

Example 4:

a) Since - 2 is "most negative" multiply both by

b) Since - 8 "most negative" multiply both by

c) Since - 9 is "most negative" multiply both by

d) Since - 7 < -3, or - 7 is "most negative" multiply by x7 or

NOTE: Where there are several terms in the numerator and several terms in the denominator separate them into a product of fractions with "same letters"

Definition of Zero Exponent a 0 = 1

Note: The result of raising any base to the 0 exponent will always be 1. (a ≠ 0)

Example 5:

1. (57x 9 y 32 z -25 )0 = 1


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