http://www.ck12.org Chapter 3. Logs and Exponents
3.2 Properties of Exponents
Here you will learn how exponents interact in a variety of algebraic situations including addition, subtraction,
multiplication and exponentiation.
It is important to quickly and effectively manipulate algebraic expressions involving exponents. One simplification
that comes up often is that expressions and numbers raised to the 0 power are always equal to 1. Why is this true
and is it always true?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/60992http://www.youtube.com/watch?v=0GAMbuPJGOY James Sousa: Properties of Exponents
Guidance
Consider the following exponential expressions with the same base and what happens through the algebraic opera-
tions. You should feel comfortable with all of these types of manipulations.
by,bx
Addition and subtraction:bx±by=bx±by
Only in the special case whenx=ycan the terms be combined. This is a basic property of combining like terms.
Multiplication:bx·by=bx+y
When the bases are the same then exponents can be added.
Division:bbxy=bx−y
The division rule is an extension of the multiplication rule with the possibility of a negative in the exponent.
Negative exponent:b−x=b^1 x
A negative exponent means reciprocal.
Fractional exponent:(b)
(^1) x
= x
√
bSquare roots are what most people think of when they think of roots, but roots can be taken with any real number
using fractional exponents.
Powers of Powers:(bx)y=bx·y
Example A
Simplify the following expression until all exponents are positive.