1. 8.1-8.3 The Rules of Exponents
Algebra
The Rules of Exponents

2. Exponent Table Property Meaning Example Product of Powers Property
Power of a Power Property
Power of a Product Property

3. Definitions
EXPONENT 5 3
BASE

4. Examples Using Product of Powers
Let’s try three together! .
1) x x = 2 4 6 x . .
2) y y y = 3 4 y 8 .
3) x y xy = 3 2 5 4 7
x y
Try these two on your own! . 8
4) = 7 3 8
5) (-6) (-6) = 4 4
(-6)

5. Examples Using Power of a Power
1) (9 ) = 3 4 12 9 3 2 6
2) [(-3) ] =
(-3)
Let’s try two together!
Try this one on your own!
3) (x ) = 2 4 x 8

6. Examples Using Power of a Product
Let’s try two together!
1) (x y ) = 3 2 3 9 6
x y
2) -(2y ) = 3 4
-16y 12
Try these two on your own!
4) (-2y ) = 3 4 12
16y 3 1 1 2 6
3) [ a b ] = 3 9
a b 27 3

7. Using All Three Properties Together
Let’s try one together! . 3 5 2 3
1) (5x y ) x = 11 9
125x y
Try this one on your own! 2 3 16 8
2) (3a b) (2a b ) = 2 4 2
72a b

8. Exponent Table Property Meaning Example Product of Powers Property
Power of a Power Property
Power of a Product Property
Zero as an Exponent
Why?
See
table.
Why?
See
table.
Negative Exponents
Dividing with Exponents
Power of a Quotient Property
Move any exponent across the fraction bar
to change the sign of the exponent.

9. [ ] Examples 1) = 3 2) = 8a b 2a b 3) a b 4b 1 1 3 = = 27 3 3
1) = -3 = 3 = 3 27 5 3 3
Let’s try two together! -2 2
[ ] 3 -2 3 4 16
2) = = -2 2 3 9 4 4
Try this one on your own!
8a b 2a b 3 -1 8 4 7 3)
= 4a b
a b b -2 4 -2

10. HW
P. 804 #1-28