Download Click here for the powerpoint review

Exponents
Location of Exponent
• An exponent is a little number high
and to the right of a regular or base
number.
Base
3
4
Exponent
Definition of Exponent
• An exponent tells how many times
a number is multiplied by itself.
Base
3
4
Exponent
What an Exponent Represents
• An exponent tells how many times
a number is multiplied by itself.
4
3 =3x3x3x3
How to read an Exponent
• This exponent is read three to the
fourth power.
Base
3
4
Exponent
How to read an Exponent
• This exponent is read three to the
2nd power or three squared.
Base
3
2
Exponent
How to read an Exponent
• This exponent is read three to the
3rd power or three cubed.
Base
3
3
Exponent
What is the Exponent?
2x2x2= 2
3
What is the Exponent?
3x3= 3
2
What is the Exponent?
5x5x5x5= 5
4
What is the Base and the
Exponent?
8x8x8x8= 8
4
What is the Base and the
Exponent?
7 x 7 x 7 x 7 x 7 =7
5
What is the Base and the
Exponent?
9x9= 9
2
How to Multiply Out an
Exponent to Find the
Standard Form
4
3 =3x3x3x3
9
27
81
What is the Base and Exponent
in Standard Form?
4
2
= 16
What is the Base and Exponent
in Standard Form?
2
3
= 8
What is the Base and Exponent
in Standard Form?
3
2
= 9
What is the Base and Exponent
in Standard Form?
5
3
= 125
Product law:
Ex:
add the exponents
together when
multiplying the powers
with the same base.
312 * 33
 312 3
 315
NOTE:
This operation
can only be
done if the
base is the
same!
Quotient law
NOTE:
Ex:
subtract the
exponents when
dividing the
powers with the
same base.
3 3
12
3
12 3
3
3
9
This
operation
can only
be done if
the base is
the same!
Power of a power:
keep the base
and multiply the
exponents.
Ex:
NOTE:
3 5
(4 )
4
4
3*5
15
Multiply
the
exponents,
not add
them!
Zero exponent law:
Any power
raised to an
exponent of
zero equals
one.
Ex:
1234123483214
1
NOTE:
No matter how big the
number is, as long as it has
zero as an exponent, it
equals to one. Except
00  1
0
Negative exponents:
Ex:
To make an
exponent positive,
flip the base.
NOTE:
This does not change the
sign of the base.
8
4
4
1
 
8
1

4096
Multiplying Polynomials:
In multiplying polynomials,
you have to multiply the
coefficients and add up the
exponents of the variables
with the same base.
Ex:
5 x
2
y
4 x
 4*5
 20
 x 2 * x3
 x5
 y * y2
 y3
 20 x 5 y 3
3
y2

Dividing polynomials:
When dividing
polynomials, you
must divide the
coefficients(if
possible) and
subtract the
exponents of the
variables with the
same base.
Ex:
25 x 5 y 4
5x 4 y 2
 25  5
 5
 x5  x 4
 x
 y4  y2
 y2
 5 x y2
Please simplify the following equations:
2
x *x
3
23
How?:
Answer:
x
5
5
Please simplify the following equations:
x  x 13  5
13
5
How?:
Answer:
x
8
8
Please simplify the following equations:
5 
5 2
Answer:
2*5
How?:
 10
510
5
 9765625
10
 9765625
Please simplify the following equations:
5
3
5
How?:
3
1
 
5
1
Answer:

125
3
3
1
 
5
 1  1  1 
    
 5  5  5 
1

125
Please simplify the following equations:
4*3
(4 x 4 y 2 )(3x 2 y 3 )
How?:
 12
 x *x
4
Answer:
6
12 x y
5
x
2
6
 y *y
2
y
3
5
 12 x y
6
5
Please simplify the following equations:
3
4
12 x y
4x2 y2
12  4
How?:
3
 x x
3
Answer:
3xy
2
2
x
 y y
4
 3 xy
2
2
Review
Copy and complete each of the
following questions.
2
b
7
b
• 1.)
*
9
• 1.) b
3
4
• 2.) (p )
12
• 2.) p
2
3
3
• 3.) (a ) * a
9
• 3.) a
• 4.) x2 * (xy)2
4
2
• 4.) x y
2
3
• 5.) (4m) * m
• 5.) 16m5
• 6.) (3a)3*(2p)2
• 6.)
3
2
108a p
• 7.)82*(xy)2*2x
3
2
• 7.) 128x y
3
4
• 8.) w * (3w)
• 8.) 81w7
• 9.) q0
• 9.) 1
• 10.) p-2
2
• 10.) 1/p
2
0
• 11.)(a b)
• 11.) 1
• 12.)(x-2y3)-2
• 12.)
4
6
x /y
•13.)
4
p
2
p
2
p
•13.)
2
•14.) 3b
5
9b
3
•14.) 1/3b
•15.)
2
2
(4x )
•15.) 4
4
4x
•16.)
2
x
0
y *
*
3
-4
x *y
4
•16.) 9y /x
2
3
•17.) m *
n
5
7
•17.) m /n
2
3
-1
•18.) 3a
2b
2
b * 3 *a
5
4
•18.) 6a /b
3
2
-4
m n
3
(3/4)
• 19)
• 19) 27/64
2
• 20) 2+3(4)
• 20) 50