5.1 Monomials
Monomial
Standard Notation
Scientific Notation
Definition of a Monomial
Monomial are one term algebraic
expression.
A term is an coefficient times a variable
to a power.
7x3 The coefficient is 7
The variable is x
The power is 3
Monomial powers are never fractions or
negative. Monomial will never a
variable as a denominator.
Negative exponents
If you remember how to multiply
variables, then learning about negative
is easier.
x x  xxxxxxxx  x
3
5
3 5
 x
8
When you multiply like variables you add
their exponents
Negative exponents
When you divide like variables you
subtract their exponents
x x 
5
3
xxxxx
xxx
 x
53
 x
2
Negative exponents
When you divide like variables you
subtract their exponents
x x 
3
5
xxx
xxxxx
 x
35

1
x
2
 x
2
Simplify with only positive exponents
 2 a b  5 ab 
3
k
2
k
10
5
;k  0
x y
2
4
Properties of Powers
Power of Power
x 
5 4
 x x x   x
 x
5
5
5
5
54
 x
20
Power of Product
ab   ab ab ab   a
3 3
3
3
3
13
b
3 3
a b
Power of Fractions
3
21
 x 
 x 7   x 7   x 7  x 7 3
x
 2    2   2   2   2 3  6
 y 
 y  y  y  y
y






7
3
9
Simplify with only positive exponents
b 
2 4
 3c
2
d
  2a 
 2 
 b 
x
 
3
4
5

5 3
Simplify with only positive exponents
  3a
 6y 4
 a b

5y




5
Scientific Notation
A way to express really big or small
number in terms of a power of ten.
Scientific Notation needs to have one
number in front of the decimal.
3,120,000 would become 3.12 X 106
0.00000451 would become 4.51 X 10-6
Write Standard Notation
in Scientific Notation
4,560,000
0.000092
You can multiply with
scientific notation
(3 X 104)(5 X 105) = (3X5)(104X105)
= 15 x 109
= 1.5 x 10 x 109
= 1.5 x 1010
You can multiply with
scientific notation
(1.8 x 10-4)(4 x 107) =
Division of scientific notation
2 . 7 X 10
3 X 10
6
4

2 .7
X
3
 0 . 9 X 10
2
 9 . 0 X 10
1
10
6
10
4
X 10  9 . 0 X 10
2
Now something from the 70’s
The power of TEN
http://www.youtube.com/watch?v=0fKBhvDjuy0
Homework
Page 226 – 228
# 19 – 59 odd
64,65, 80 – 84 even
Homework
Page 226 – 228
# 18 – 60 even
79, 81, 83