Transcript Lesson 5.1

Bellringer #1
 Write
each using exponential notation
1) 8 ∙ 8 ∙ 8 ∙ 8 =
𝟒
𝟖
2)12 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 =
𝟑
𝟏𝟐𝒃
 Evaluate
4
each expression
3) 𝑚 − 5 𝑓𝑜𝑟 𝑚 = 2
2
4) 3𝑏 𝑓𝑜𝑟 𝑏 = 4
11
48
5.1 Exponents
Zero Exponent Property
Rule:
*𝑎 ≠ 0
0
𝑎 =1
Examples
0
1. 10
=1
0
2. (−5)
=1
0
3. −4
0
-(4 )
0
4. 𝑥
=
=1
=-1
Multiplying Using Exponents
83 • 82 means (8•8•8)(8•8)= 85
52 • 54 means (5•5)(5•5•5•5) = 56
What did we do with the exponents?
Added them
Product of Powers Propoerty
Rule:
a a  a
m
n
m n
*When the bases are the same,
add the exponents.
Example 1
8 8
4
8
43
8
7
3
Example 2
a a
5
a
5 3
a
8
3
Example 3
y y y
3
2
y
3 2  5
y
10
5
Example 4
2
4
6
(mn )(m n )
(m  m )(n  n )
1
4
1 5
(m
2
)(n
2 6
6 8
mn
6
)
Quotient of Powers Property
Rule:
m
a
mn

a
n
a
*When the bases are the same,
subtract the exponents.
Example 5
5
4
2
4
5 2
4
4
3
Example 6
6
x
2
x
62
x
x
4
Example 7
p q
2
5
p q
5
7
5
7
p q
( 2 )( 5 )
p q
(p
5 2
)(q
3
pq
2
7 5
)
Example 8
5
g
5
g
g
55
g 1
0
Negative Exponent Property
Rule:
a
m
1
 m
a
* NEVER leave negative
exponents in your answers!!
Example 9
Express using positive exponents.
2
4
1
2
4
Example 10
Express using positive exponents.
3
5m
5
3
m
Example 11
Express using positive exponents.
1
ab
a
1
b
Example 12
Simplify.
2
3
1
2
3
1
9
Example 13
Simplify.
4
1
1
4
1
1
1
1
Example 15
Simplify.
(2) (2)
2
(2)
2 4
(2)
64
6
4
Example 16
Simplify.
(3)
4
(3)
6
(3)
6 4
(3)
9
2
Example 17
Simplify.
3
4
5
4
3 5
4
4
2
1
1

2
4 16
Assignment
Pg. 207 #’s 1 – 66 all