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	Miscellaneous Equations
	Operations with Fractions
	Undefined Rational Expressions
	Inequalities
	Writing Equations for Lines Using Sequences
	Intersections of Lines and Conics
	Graphing Linear Equations
	Solving Equations with Log Terms and Other Terms
	Quadratic Expresions - Complete Squares
	Adding and Subtracting Fractions with Like Denominators
	Multiplying a Fraction by a Whole Number
	Solving Equations with Log Terms and Other Terms
	Solving Quadratic Equations by Factoring
	Locating the Solutions of the Quadratic Equation
	Properties of Exponents
	Solving Equations with Log Terms on Each Side
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	Graphs of Trigonometric Functions
	Estimating Products and Quotients of Mixed Numbers
	Inequalities
	The circle
	Adding Polynomials
	Adding Fractions with Unlike Denominators
	Factoring Polynomials
	Linear Equations
	Powers of Ten
	Straight Lines
	Dividing With Fractions
	Multiplication Property of Equality
	Rationalizing Denominators
	Multiplying And Dividing Fractions
	Distance Between Points on a Number Line
	Solving Proportions Using Cross Multiplication
	Using the Quadratic Formula
	Scientific Notation
	Imaginary Numbers
	Values of Symbols for Which Fractions are Undefined
	Graphing Equations in Three Variables
	Writing Fractions as Decimals
	Solving an Equation with Two Radical Terms
	Solving Linear Systems of Equations by Elimination
	Factoring Trinomials
	Positive Rational Exponents
	Adding and Subtracting Fractions
	Negative Integer Exponents
	Rise and Run
	Brackets
	Multiplying Square Roots
	Multiplying Polynomials
	Solving Systems of Linear Inequalities
	Multiplication Property of Radicals
	A Quadratic within a Quadratic
	Graphing a Linear Equation
	Calculations with Hundreds and Thousands
	Multiplication Property of Square and Cube Roots
	Solving Equations with One Log Term
	The Cartesian Coordinate Plane
	Equivalent Fractions
	Adding and Subtracting Square Roots
	Solving Systems of Equations
	Exponent Laws
	Solving Quadratic Equations
	Factoring Trinomials
	Solving a System of Three Linear Equations by Elimination
	Factoring Expressions
	Adding and Subtracting Fractions
	The parabola
	Computations with Scientific Notation
	Quadratic Equations
	Finding the Greatest Common Factor
	Introduction to Fractions
	Simplifying Radical Expressions Containing One Term
	Polynomial Equations
	Graphing and Intercepts
	The Number Line
	Adding and Subtracting Rational Expressions with Different Denominators
	Scientific Notation vs Standard Notation
	Powers
	Factoring by Grouping
	Extraneous Roots
	Variables and Expressions
	Linera Equations
	Integers and Substitutions
	Squares and Square Roots
	Adding and Subtracting Rational Expressions with Different Denominators
	Solving Linear Inequalities
	Expansion of a Product of Binomials
	Powers and Exponents
	Finding The Greatest Common Factor
	Quadratic Functions
	The Intercepts of a Parabola
	Solving Equations Containing Rational Expressions
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	Subtracting Polynomials
	Solving Equations
	Adding Fractions with Unlike Denominators
	Solving Systems of Equations by Substitution
	Solving Equations
	Product and Quotient of Functions

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Properties of Exponents

The table below summarizes the properties of exponents.

Property	Positive Integer Exponents	Negative Integer Exponents
Multiplication x^m Â· xⁿ = x^m+n	3² Â· 3⁴ = 3²⁺⁴ = 3⁶
Division Here, x ≠ 0.
Power of a Power (x^m)ⁿ = x^mÂ·n	(5²)³ = 5²^Â·3 = 5⁶	(5^-2)^-3 = 5^(-2)^Â·(-3) = 5⁶
Power of a Product (x Â· y)ⁿ = xⁿ Â· yⁿ	(5 Â· 7)³ = 5³ Â· 7³
Power of a Quotient Here, y ≠ 0.

The properties of exponents can be used to derive the following two formulas:

Formulas

Negative Exponents and Fractions

When a factor is moved to the other side of the fraction bar, we change the sign of the exponent.

Here, x ≠ 0 and y ≠ 0.

A fraction raised to a power is equal to the reciprocal of the fraction raised to the opposite power.

Here, x ≠ 0 and y ≠ 0.

We can use these formulas to rewrite expressions using positive exponents.