1. 5.1 Using Properties of Exponents
Algebra II

2. Properties of Exponents a&b are real numbers, m&n are integers
Product Property: am * an=am+n
Power of a Power Property: (am)n=amn
Power of a Product Property: (ab)m=ambm
Negative Exponent Property: a-m= ; a≠0
Zero Exponent Property: a0=1; a≠0
Quotient of Powers: am = am-n; a≠ an
Power of Quotient: b≠0

3. Example 1 – Product Property
(-5)4 * (-5)5 =
(-5)4+5 =
(-5)9 =

4. Example 2
x5 * x2 =
x5+2 = x7

5. Example 3 – Power of a Power
(23)4 =
23*4 =
212 =
4096

6. Example 4
(34)2 =
34*2 =
38 =
6561

7. Example 5 – Neg. Exponent
(-5)-6(-5)4 =
(-5)-6+4 =
(-5)-2 =

8. Example 6 – Quotient of Powers

9. Example 7 – Power of Quotient

10. Example 8 – Zero Exponent
(7b-3)2 b5 b =
72 b-3*2 b5 b =
49 b =
49b0 = 49

11. Example 9 – Quotient of Powers

12. Ex. 10 – Scientific Notation
131,400,000,000 =
5,284,000
When multiplying or dividing scientific notation, multiply or divide the c value and use appropriate property for the base 10.
1.314 x 1011 =
5.284 x 106

13. How many places did you have to move the decimal?
Scientific Notation
131,400,000,000=
1.314 x 1011
Put that number here!
Move the decimal behind the 1st number
How many places did you have to move the decimal?

14. Assignment