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	Calculations with Negative Numbers
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	Evaluating Expressions and Solving Equations
	Fraction rules
	Factoring Quadratic Trinomials
	Multiplying and Dividing Fractions
	Dividing Decimals by Whole Numbers
	Adding and Subtracting Radicals
	Subtracting Fractions
	Factoring Polynomials by Grouping
	Slopes of Perpendicular Lines
	Linear Equations
	Roots - Radicals 1
	Graph of a Line
	Sum of the Roots of a Quadratic
	Writing Linear Equations Using Slope and Point
	Factoring Trinomials with Leading Coefficient 1
	Writing Linear Equations Using Slope and Point
	Simplifying Expressions with Negative Exponents
	Solving Equations 3
	Solving Quadratic Equations
	Parent and Family Graphs
	Collecting Like Terms
	nth Roots
	Power of a Quotient Property of Exponents
	Adding and Subtracting Fractions
	Percents
	Solving Linear Systems of Equations by Elimination
	The Quadratic Formula
	Fractions and Mixed Numbers
	Solving Rational Equations
	Multiplying Special Binomials
	Rounding Numbers
	Factoring by Grouping
	Polar Form of a Complex Number
	Solving Quadratic Equations
	Simplifying Complex Fractions
	Algebra
	Common Logs
	Operations on Signed Numbers
	Multiplying Fractions in General
	Dividing Polynomials
	Polynomials
	Higher Degrees and Variable Exponents
	Solving Quadratic Inequalities with a Sign Graph
	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
	Solving Linear Equations
	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
	fractions
	Rotating an Ellipse
	Multiplying Numbers
	Linear Equations
	Solving Equations with One Log Term
	Combining Operations
	The Ellipse
	Straight Lines
	Graphing Inequalities in Two Variables
	Solving Trigonometric Equations
	Adding and Subtracting Fractions
	Simple Trinomials as Products of Binomials
	Ratios and Proportions
	Solving Equations
	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
	Solving Quadratic Equations
	Dividing and Subtracting Rational Expressions
	Square Roots and Real Numbers
	Order of Operations
	Solving Nonlinear Equations by Substitution
	The Distance and Midpoint Formulas
	Linear Equations
	Graphing Using x- and y- Intercepts
	Properties of Exponents
	Solving Quadratic Equations
	Solving One-Step Equations Using Algebra
	Relatively Prime Numbers
	Solving a Quadratic Inequality with Two Solutions
	Quadratics
	Operations on Radicals
	Factoring a Difference of Two Squares
	Straight Lines
	Solving Quadratic Equations by Factoring
	Graphing Logarithmic Functions
	Simplifying Expressions Involving Variables
	Adding Integers
	Decimals
	Factoring Completely General Quadratic Trinomials
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Rational Expressions With Unlike Denominators
	Rational Exponents
	Horizontal and Vertical Lines

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Properties of Exponents

Example 1

Write without using a negative exponent: (5x³)^-²y⁴

Solution	(5x³)^-²y⁴
Use the Power of a Product Property.	= (5¹)^-2 Â· (x³)^-2 Â· y⁴
Use the Power of a Power Property.	= 5¹^(-2) Â· x³^(-2) Â· y⁴
Simplify.	= 5^-2 Â· x^-6 Â· y⁴
Use the definition .
Write 5² as 25.

So, the result is .

Example 2

Simplify

. Write your answer using positive exponents.

Solution
Reduce the common factor of 16.
Use the property to rewrite using only positive exponents.
Use the Multiplication Property (add exponents).
So, the result is .

Example 3

Simplify

. Write your answer using positive exponents.

Solution
Use to rewrite using positive exponents.
Use the Power of a Quotient Property.
Use the Power of a Product Property.
Simplify.
So, the result is .

Note:

We usually write the negative sign outside of the fraction. Thus, is written as .