Download 02-14 4.2 Exponents

§4.2 Exponents
2/14/17
Today We’ll Discuss
How do we define exponentiation?
What are properties of exponents?
Brave New World…
Of Operations
We have traversed the land of the four
basic operations (+, −, •, ÷) and discovered
new territory.
Exponents are the first operation students
learn that has a very different form of
notation.
But first, what’s the motivation??
PAST-CAM
●ON
Defining Multiplication
Definition: Let n and a be two whole
numbers (n ≠ 0). The product of n and a,
written as n • a, is the whole number such
that
n•a=a+a+a+...+a
n addends
The numbers n and a are the factors of the
product.
Defining Exponentiation
Definition: Let a and m be natural
numbers. The power of m factors of a is
written in exponential form like such:
am = a • a • a • . . . • a
m factors
where a is the base, m is the exponent, and
the am is the power.
More Common Vocabulary
The expression
am
is read as “a to the mth.”
More Common Vocabulary
The expression
45
is read as “4 to the 5th.”
More Common Vocabulary
The expression
32
is read as “3 squared.”
More Common Vocabulary
The expression
73
is read as “7 cubed.”
Example
Use the definition of exponentiation to find
a) 33
b) 26
Rewrite the following using more compact
notation:
a) x•x•x•x•x•x•x
b) x+x+x+x+x
Understanding Special Exponents
Paper
Time!
Special Exponents
For any natural number a,
0
a
=1
1
a =a
Note: 00 is Undefined!!!!
Product of Powers
What is 23?
What is 24?
What is 23•24?
Product of Powers
To multiply two powers having the same
base, keep the base and add the
exponents.
m
n
a •a
=
m+n
a
Quotient of Powers
What is 34?
What is 32?
What is 34/32?
Quotient of Powers
To divide two powers having the same
base, keep the base and subtract the
exponents.
m
n
a /a
=
m−n
a
Example
Simplify each expression to a single power
without multiplying or dividing.
a) 103•104
b) 86/82
c) 927•93•910
d) x9000/x9
Power of a Product
Now take a look at
4
(a•b)
Use the definition to write this out, then
simplify. What property does this
demonstrate?
Power of a Product
To find the power of a product, you can
find the power for each factor and then
multiply.
m
(a•b)
=
m
m
a •b
Example
Write each expression as a single power.
Write which property you used. If not
possible, write “not possible.”
a) 35•45
b) 23•26
c) 57•87
d) 43•102
Power of a Power
Now take a look at
3
4
(b )
Use the definition to write this out, then
simplify. What property does this
demonstrate?
Example
Write each expression as a single power.
Then evaluate the power.
a) (24)2
b) (83)0
Example
Write each expression as a product of two
powers.
a) (23a)2
b) (5c2)5
Homework #8 Section §4.2
Pages 140-143
#6,8,10,14,19,22,24,26,30,36