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 7The variable is xThe 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.

When you multiply like variables you add their exponents

85353 xxxxxxxxxxxx

Negative exponents

When you divide like variables you subtract their exponents

23535 xxxxx

xxxxxxx

Negative exponents

When you divide like variables you subtract their exponents

22

5353 1

x

xx

xxxxx

xxxxx

Simplify with only positive exponents

43 52 abba

0;10

2

kk

k

25 yx

Properties of Powers

Power of Power

Power of Product

Power of Fractions

2045555545 xxxxxxx

93333133333 babaabababab

6

21

32

37

2

7

2

7

2

73

2

7

y

x

y

x

y

x

y

x

y

x

y

x

Simplify with only positive exponents

3523 dc

5

2

2

b

a

4

3

x

42b

Simplify with only positive exponents

5

46

53

ba

ay

y

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

100.910100.9

109.0

10

10

3

7.2

103

107.2

21

2

4

6

4

6

XXX

X

XX

X

Now something from the 70’s

The power of TEN

http://www.youtube.com/watch?v=0fKBhvDjuy0

Homework

Page 226 – 228# 19 – 59 odd64,65, 80 – 84 even

Homework

Page 226 – 228# 18 – 60 even

79, 81, 83