Page 214 - Algebra 1

The Quotient Property of Exponents is used when dividing algebraic expressions. This property states that to divide two algebraic expressions with the same base, subtract their exponents.
Quotient Property of Exponents
If m and n are real numbers and x ≠ 0, then
_m _ x =xm-n= 1
xn xn-m _4
5 = 1 = 1 = 1 _2 ___
54 54-2 52 25
5 = 54-2 = 52 = 25 52
Example
3
Using the Quotient Property of Exponents
Simplify each expression. All variables represent nonzero real numbers. _7
Math Reasoning
Analyze Why is _x5 = x4? x
a. x x3
SOLUTION
_7
x x3
= x7-3 = x4
Quotient Property of Exponents Simplify.
Quotient Property of Exponents Simplify.
Quotient Property of Exponents Simplify.
Write with only positive exponents.
b. x x-7
x x-7
= x3-(-7) = x10
_3
SOLUTION
_3
Math Reasoning
Analyze Use the Quotient Property of Exponents to show another method for
simplifying _x-5 . x
_-5 6 xyz
c.
z-3y2x SOLUTION
_-5 6 xyz
z-3y2x
= x-5-1y6-2z1-(-3)
= x-6y4z4 _4 4
=yz x6
Lesson 32 199