FreeAlgebra                             Tutorials!  
Home
Polynomials
Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Factoring
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
index casa mío
Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 

Zero Power Property of Exponents

Property — Zero Power Property

English Any real number, except zero, raised to the power 0 is 1.

Algebra x0 = 1, x 0

Example 170 = 1

Here’s a way to understand why 170 is 1.

Suppose we write 0 as 2 - 2. Then, 170 = 172 - 2.

By the Division Property of Exponents,

Since 170 = 172 - 2 and 172 - 2 = 1, we have 170 = 1.

Note:

This same reasoning applies no matter what power or nonzero base we choose.

Therefore, x0 = 1 for x 0.

 

Example 1

a. Use the Zero Power Property to simplify 50.

b. Justify your answer.

Solution

a. Any real number, except zero, raised to the power 0 is 1. 50 = 1

b. Suppose we have

We can simplify this using the Division Property of Exponents.

But if we reduce the fraction the result is 1.

Since is equivalent to both 50 and 1, we conclude 50 = 1.

 

Example 2

Find each of the following. (Assume each variable represents a nonzero real number).

a. (-7)0 b. c. (12x4y5)0 d. -2y0 e. 00

Solution

In each case, we apply the Zero Power Property: any nonzero real number raised to the zero power is 1.
a. The base is the real number -7. (-7)0 = 1
b. The base, w, represents a nonzero real number.
c. The base, 12x4y5, represents a nonzero real number. (12x4y5)0 = 1
d. Only y is raised to the power 0. -2y0 = -2 · 1 = -2
e. In the Zero Power Property, the base cannot be 0.  00 is undefined
All Right Reserved. Copyright 2005-2014