8.3 Notes Diiorio.notebook
March 31, 2016
Lesson 8.3 Division Properties of Exponents 45
43
=
. . . .
4 4 4 4 4
. .
4 4 4
. = 45 ­ 3 = 42
= 4 4
Apr 19­8:23 PM
1
8.3 Notes Diiorio.notebook
March 31, 2016
Division Properties of Exponents Quotient of Powers Property: To divide powers having the same base, subtract exponents. am
=a
m­n
, a≠0
an
Power of a Quotient Property: To find a power of a quotient, find the power of the numerator and the power of the denominator and divide. am
a m
b ≠ 0
= m
b
b
Apr 19­8:40 PM
2
8.3 Notes Diiorio.notebook
March 31, 2016
Example 1: Using the Quotient of Power Property 1
6
5
64
­5
5
2
­ 2
9 .9
4 2
9
7
. y3
y5
Apr 19­8:38 PM
3
8.3 Notes Diiorio.notebook
March 31, 2016
Example 2: Using the Power of a Quotient Property 2
3
2
­
3
3
y
7
­3
4
Apr 19­9:19 PM
4
8.3 Notes Diiorio.notebook
March 31, 2016
Example 3: Simplifying Expressions
2x2y
3x
.
2x
9xy2
4
y2
y
2
Apr 19­9:30 PM
5
8.3 Notes Diiorio.notebook
March 31, 2016
Example 4: Using the Quotient of Powers Property
The number of shares N (in billions) listed on the New York Stock Exchange from 1977 through 1997 can be modeled by N = 92.56 (1.112)t where t = 0 represents 1990. Find the ratio of shares listed in 1997 to the shares listed in 1977. Apr 19­9:37 PM
6
8.3 Notes Diiorio.notebook
March 31, 2016
Example 5: Using the Power of a Quotient Property You toss a fair coin ten times. Show that the probability that the coin lands on heads up each time is about 0.001. Apr 19­9:42 PM
7