Transcript 5.1 Monomials
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.
7x 3 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
3
x
5
x
x
x
x
x
x
x
x
x
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
5
x
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
3
x
5
x
x
x
x
x x
x
x
x
3 5 1
x
2
x
2
Simplify with only positive exponents 2
a
3
b
5
ab
4
k
2
k
10 ;
k
0
x
5
y
2
Properties of Powers
x
Power of Power
x
5 4
x
20 Power of Product
a
1 3
b
3 3
a
3
b
9 Power of Fractions
x
7
y
2 3
x
7
y
2
x
7
y
2
x
7
y
2
x
7 3
y
2 3
x
21
y
6
Simplify with only positive exponents 4 3
c
2
d
5 3 2
a b
2 5
x
3 4
Simplify with only positive exponents
a
6 3
a
5
y b
4
y
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 10 6 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 10 4 )(5 X 10 5 ) = (3X5)(10 4 X10 5 ) = 15 x 10 9 = 1.5 x 10 x 10 9 = 1.5 x 10 10
You can multiply with scientific notation (1.8 x 10 -4 )(4 x 10 7 ) =
Division of scientific notation 2 .
7
X
10 6 3
X
10 4 2 .
7
X
3 10 6 10 4 0 .
9
X
10 2 9 .
0
X
10 1
X
10 2 9 .
0
X
10
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