1. Algebra 1
Section 8.2

2. Properties of Exponents
Quotient Property: = xa-b xa xb
Negative exponent: x-a = 1 xa

3. Example 2
Simplify
24x2y6z7
-8xy2z5 -3
x2-1
y6-2
z7-5
-3xy4z2

4. Properties of Exponents
Since x-a = , we also know 1 xa
that = xa. 1
x-a
a-2 = 1 a2
= 52 1
5-2

5. Example 3 1 x4
y2 = y2 x4
a. x-4y2 = 1 x2
2( ) = 2 x2
b. 2x-2 =

6. Example 3
c. (-3x-2)3 =
(-3)3x-2(3) =
-27x-6 = 1 x6
-27( ) = 27 x6

7. Example 3
d. ( x-3)-2 = 1 3
( )-2x-3(-2) = 1 3
32x6 =
9x6

8. Properties of Exponents
Quotient Property: = xa-b xa xb
Negative exponent: x-a = 1 xa
Zero exponent: x0 = 1

9. Example 4 Divide and express the answer in positive exponential form.
34x-3y2z-5
-18x-6y2z-2 34 18
x-3-(-6)
y2-2
z-5-(-2) 17 9 =
17x3
9z3 =
17x3(1)
9z3 x3 y0
z-3

10. Properties of Exponents
The power of a quotient is equal to the quotient of the powers: a b = an bn n
( )

11. ( ) Example 5 Simplify, leaving all variables in the numerator: y x2
(x3y-4)2 3
( )
x6-6y3+(-8)
x0y-5 y3 x6
(x6y-8)
y-5

12. Properties of Exponents
An expression containing negative exponents in the denominator is not considered to be simplified.
It is generally preferable to use only positive exponents in a simplified expression.

13. Homework: pp