1. 6.1 Properties of Exponents
2/4/2013

2. Power, Base and Exponent:73
Exponent: is the number that tells you how many times the base is multiplied to itself.
In this example 73 means 7•7•7

3. In general: am•an = am+n
Product of Powers:
Ex. 32 • 35
= 3•3•3•3•3•3•3
= 37
= 32+5
In general: am•an = am+n

4. In general: (am)n = am•n
Power of a Power:
Ex. (23 )2
= (23 )• (23 )
=(2•2•2)•(2•2•2)
= 26 = 23•2
In general: (am)n = am•n

5. In general: (a •b)m =a m•b m
Power of a Product:
Ex. (4•3 )3
= (4•3 )• (4•3 ) • (4•3 )
=(4•4•4)•(3•3•3)
= 4 3 •3 3
In general: (a •b)m =a m•b m

6. In general: a0 = 1 Zero Exponent 50 = 1 40 = 1 30 = 1 ÷5 ÷5 ÷5 ÷4 ÷4÷3 ÷3 ÷3
In general: a0 = 1
Any base raised to a 0 power equals 1.

7. Exponential Form Fraction Form
32 9
31 3
30 1 = =

8. Ex. 5-2 Ex. In general: Negative Exponent
Negative exponent MOVES power.
If the power with a negative exponent is in the numerator, the power moves to the denominator and exponent becomes positive.
If the power with a negative exponent is in the denominator, the power moves to the numerator and exponent becomes positive.

9. Quotient of Powers
Ex.
In general:

10. Power of a Quotient
Ex.
In general:

11. Example 1 ( ) 8 2 – )4 = ( ) 8 4 2 – + = ( ) 4 2 – 1 ( )4 2 – = = 16 1
Evaluate Expressions with Negative Exponents (
) 8 2 – )4
Product of powers property = ( ) 2 – + = (
) 4 2 –
Simplify exponent. 1 ( )4 2 – =
Negative exponent property = 16 1
Evaluate power.

12. Example 2 33 35 2 Evaluate . 33 35 2 = ( )2 32 = 34 = 81
Evaluate Quotients with Exponents 33 35 2
Evaluate
Quotient of powers property 33 35 2 = ( )2 32 = 34
Power of a power property = 81
Evaluate power. 12

13. Evaluate the expression.
Checkpoint
Evaluate Numerical Expressions
Evaluate the expression. 1. ( )3 22
ANSWER 64 ( )3 50 2.
ANSWER 1
ANSWER 27 1 – 3. (
) 5 3 – )2 4. 3 2
ANSWER 27 8

14. Example 3 a. y x – 3 2 x 2 ( )2 y – 3 = = x 2 y – 3 2 • = x 2 y – 6 =
Simplify Algebraic Expressions a. y x – 3 2
Power of a quotient property
x 2 ( )2 y – 3 = =
x 2 y –
3 2 •
Power of a power property =
x 2 y – 6
Simplify exponent. =
x 2y 6
Negative exponent property

15. Example 3 ( )2 5y – 3 y 5y b. = ( )2 y – 3 y 5y 52 = 25y y 5y – 3 2 •
Simplify Algebraic Expressions ( )2 5y – 3
y 5y b. = ( )2 y – 3
y 5y 52
Power of a product property =
25y
y 5y –
3 2 •
Power of a power property =
25y
y 5y – 6
Simplify exponent. =
25y – +
Product of powers property =
25y 0
Simplify exponent. = 25
Zero exponent property 15

16. Example 3 c. x 5y 2 – x 3y 6 = x – 3 5 y 6 ( 2) = x 2y 8 – = y 8 x 2
Simplify Algebraic Expressions c.
x 5y 2 –
x 3y 6 = x – y
6 ( 2)
Quotient of powers property =
x 2y 8 –
Simplify exponent. =
y 8
x 2
Negative exponent property 16

17. Simplify the expression. ANSWER
Checkpoint
Simplify Algebraic Expressions
Simplify the expression.
ANSWER 5. ( )3 2p
p 4
8p 7 6.
xy 4 –
x 5y 3
x 4y 7
27b 2 7. ( )3 3b – 2
b 8 – s
r 2 4 3 1
r 6s 12 8.

18. Homework:
6.1 p.299 #8-34 even Disregard direction that says. “Tell which properties you used”