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Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Point
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Exponents
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
Inequalities
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Point
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

Roots and Powers

The Relationship Between Roots and Powers

 

Property — Taking the nth Root of an nth Power

    Examples  
if n is an odd positive integer and x is any real number.  
if n is an even positive integer and x ≥ 0.  
if n is an even positive integer and x < 0. = -1(-17)

= 17

 

Example 1

Simplify:

Solution

Use this relationship to simplify each radical:

 

Example 2

Simplify:

Solution

This has the form where x < 0.

Therefore, use this relationship: = -1 · x.