Powers

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	Home
	Exponential Functions
	Powers
	Linera Equations
	Simple Trinomials as Products of Binomials
	Laws of Exponents and Dividing Monomials
	Solving Equations
	Multiplying Polynomials
	Multiplying and Dividing Rational Expressions
	Solving Systems of Linear Inequalities
	Mixed-Number Notation
	Linear Equations and Inequalities in One Variable
	The Quadratic Formula
	Fractions and Decimals
	Graphing Logarithmic Functions
	Multiplication by 111
	Fractions
	Solving Systems of Equations - Two Lines
	Solving Nonlinear Equations by Factoring
	Solving Linear Systems of Equations by Elimination
	Rationalizing the Denominator
	Simplifying Complex Fractions
	Factoring Trinomials
	Linear Relations and Functions
	Polynomials
	Axis of Symmetry and Vertices
	Equations Quadratic in Form
	The Appearance of a Polynomial Equation
	Subtracting Reverses
	Non-Linear Equations
	Exponents and Order of Operations
	Factoring Trinomials by Grouping
	Factoring Trinomials of the Type ax 2 + bx + c
	The Distance Formula
	Invariants Under Rotation
	Multiplying and Dividing Monomials
	Solving a System of Three Linear Equations by Elimination
	Multiplication by 25
	Powers of i
	Solving Quadratic and Polynomial Equations
	Slope-intercept Form for the Equation of a Line
	Equations of Lines
	Square Roots
	Integral Exponents
	Product Rule for Radicals
	Solving Compound Linear Inequalities
	Axis of Symmetry and Vertices
	Multiplying Rational Expressions
	Reducing Rational Expressions
	Properties of Negative Exponents
	Fractions
	Numbers, Factors, and Reducing Fractions to Lowest Terms
	Solving Quadratic Equations
	Factoring Completely General Quadratic Trinomials
	Solving a Formula for a Given Variable
	Factoring Polynomials
	Decimal Numbers and Fractions
	Multiplication Properties of Exponents
	Multiplying Fractions
	Multiplication by 50

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Powers, or exponents begin as shorthand notation for repeated multiplication. For example, we write:

Here, 2 is called the base and 5 is called the power or exponent. We describe 2⁵ as meaning “2 raised to the power 5” here. The exponent applies only to the quantity to its immediate lower left. Be careful indicating powers of negative numbers. Brackets must be used:

(-3)⁴ = (-3) × (-3) × (-3) × (-3) = + 81

But, without the brackets

-3⁴ =-3 × 3 × 3 × 3 = - 81

Without the brackets, the power of 4 in -3⁴ applies only to the 3, and does not include the minus sign.