Download MFCR- Notes Exponents and scientific notation

Bell Work 12/10
Objectives
The student will be able to:
1. multiply monomials.
2. simplify expressions with monomials.
A monomial is a
1. number,
2. variable, or
3. a product of one or more
numbers and variables.
Examples:
5
y
3x2y3
Why are the following not
monomials?
x+y
addition
x
y
division
2 - 3a
subtraction
Multiplying Monomials
When multiplying monomials, you
ADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7
Simplify
1.
2.
3.
4.
m7
m8
12
m
13
m
3
4
m (m )(m)
Power of a Power
When you have an exponent with an
exponent, you multiply those exponents.
1) (x2)3
x2• 3
x6
2) (y3)4
y12
Simplify
1.
2.
3.
4.
p2
p4
8
p
16
p
2
4
(p )
Power of a Product
When you have a power outside of the
parentheses, everything in the
parentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2
Power of a Monomial
This is a combination of all of the other
rules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9
Simplify
1.
2.
3.
4.
12a8b12
81a6b7
16
81
81a b
8
12
81a b
2
3
4
(3a b )
Bell Work 12/12
Simplify
 -3x y 
 2xy 
2
1 2
3 3
Objectives
The student will be able to:
1. divide monomials.
2. simplify negative exponents.
Dividing Monomials
When dividing monomials, subtract the
exponents.
5
b
bbbbb
5-2
3
1. 2 
=b =b
b
bb
7
5
m
n
6
3
7-1
5-2
2.
n =m n
2 = m
mn
3 7
xy
3. 2 6
xy
3
7
x y
3 2 7 6 = xy
x y
2 6
x y
8 3
81a b
4.
5
9a b
8 3
81a b
8-5 3-1
3
2

9a
b
= 9a b
5
9a b
Here’s a tricky one!
3 3
3m n
5.
3 2
3m n
=
0
1m n
=n
What happened to the m?
3 3
3m n
3m m m n n n

3 2
3m n
3m m m n n
3
They canceled out! m
1
3
m
There are no m’s left over!
This leads us to our next rule…
Zero Exponents
Anything to the 0 power is equal to 1.
a0 = 1
True or False?
Anything divided by itself equals one.
True!
See for yourself!
3
1
3
x
1
x
m3
1
3
m
3 1
x 1
m 1
0
0
0
Negative Exponents
A negative exponent means you move the
base to the other side of the fraction and
make the exponent positive.
-n
n
a
1
1 a
n
a 
 n or -n  = a
1 a
a
1
-n
Notice that the base with the negative
exponent moved and became positive!
Simplify.
6.
-4
0
x y
You can not have negative or zero
exponents in your answer.
1
-4
0
x  4 and y  1
x
1
4
x
1
1 4
x
Simplify
1. p2
2. p12
1
3. p 2
1
4. p
.
12
.
-7
p
-5
p
4 2
Simplify.
3r s
1 4  3 2  4 1 2
r
 r s  rs  2
7.
3 4
6
6
6s
18r s
You can’t leave the
negative exponent!
There is another way of doing this without
negative exponents.
If you don’t want to see it, skip the next
slide!!!
Simplify.
3
x
8. 4
x
Get rid of the negative exponent.
3
x
1
1


7
4
3 4
x
x
xx
5 2
Simplify.
r s Get rid of the negative exponents.
9. 3 3
rs
5 2
3
r s
s
s


3 3
5 3 2
8
r
rs
rrs
Simplify.
x y 
4x 
2 2
3
10.
2 3
x y
3

2 2
 4x 
2 3
6 4
Get rid of the parentheses.
6 4
x y
 3 6
4 x
Get rid of the
negative exponents.
y
x y
y
 3 6  3 6 6 
12
4 x
4x x
64x
4
4
 -3x y 
Simplify
 2xy 
2
1 2
3 3
1.
2.
3.
4.
.
.
.
9x
8y11
-9x
8y11
-9x
8y7
9x
8y7
.
Objective
The student will be able to:
express numbers in scientific and
decimal notation.
How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal
notation. When numbers get this large,
it is easier to write them in scientific
notation.
Scientific Notation
A number is expressed in scientific
notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
Write the width of the universe in
scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make
this number be between 1 and 10?
Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the
decimal?
23
When the original number is more than 1,
the exponent is positive.
The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 10?
9.02
The decimal was moved how many places?
8
When the original number is less than 1, the
exponent is negative.
9.02 x 10-8
Write 28750.9 in scientific notation.
1.
2.
3.
4.
2.87509 x 10-5
2.87509 x 10-4
2.87509 x 104
2.87509 x 105
2) Express 1.8 x 10-4 in decimal
notation.
0.00018
3) Express 4.58 x 106 in decimal notation.
4,580,000
Write (2.8 x 103)(5.1 x 10-7) in
scientific notation.
1.
2.
3.
4.
14.28 x 10-4
1.428 x 10-3
14.28 x 1010
1.428 x 1011
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
4) 234.6 x
9
10
2.346 x 1011
5) 0.0642 x 104
6.42 x 10 2
Write 531.42 x 105 in scientific
notation.
1.
2.
3.
4.
5.
6.
7.
.53142 x 102
5.3142 x 103
53.142 x 104
531.42 x 105
53.142 x 106
5.3142 x 107
.53142 x 108