Bell Work 12/10

ObjectivesThe student will be able to:

1. multiply monomials.

2. simplify expressions with monomials.

A monomial is a1. 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 + yaddition

division

2 - 3a

subtraction

x

y

Multiplying MonomialsWhen multiplying monomials, you

ADD the exponents.

1) x2 • x4

x2+4

x6

2) 2a2y3 • 3a3y4

6a5y7

Simplify m3(m4)(m)

1. m7

2. m8

3. m12

4. m13

Power of a PowerWhen you have an exponent with an

exponent, you multiply those exponents.

1) (x2)3

x2• 3

x6

2) (y3)4

y12

Simplify (p2)4

1. p2

2. p4

3. p8

4. p16

Power of a ProductWhen 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 MonomialThis is a combination of all of the other

rules.

1) (x3y2)4

x3• 4 y2• 4

x12 y8

2) (4x4y3)3

64x12y9

Simplify (3a2b3)4

1. 12a8b12

2. 81a6b7

3. 81a16b81

4. 81a8b12

Bell Work 12/12

22 1

33

-3x

2x

y

y

Simplify

ObjectivesThe student will be able to:

1. divide monomials.

2. simplify negative exponents.

When dividing monomials, subtract the exponents.

1.

2.

Dividing Monomials

= m6 n3

5

2

b

b

7 5

2

m n

mn

= b5-2b b b b b

b b

= b3

= m7-1n5-2

= xy

3. x3y7

x2 y6

4. 81a8b3

9a5b

= 9a3b2

8 38-5 3-1

5

81a b9a b

9a b

672362

73 yx

yx

yx

5. 3m3n3

3m3n2 = 1m0n

Here’s a tricky one!

What happened to the m?

= n

3 3

3 2

3m n 3m m m n n n

3m n 3m m m n n

They canceled out!

There are no m’s left over!This leads us to our next rule…

3

31

m

m

Zero ExponentsAnything to the 0 power is equal to 1.

a0 = 1True or False?

Anything divided by itself equals one.True!

See for yourself!

3

3

3 x m1 1 1

3 x m

0 0 03 1 x 1 m 1

A negative exponent means you move the base to the other side of the fraction and make the exponent positive.

-n n-n n

n -n

a 1 1 aa or = a

1 a a 1

Negative Exponents

Notice that the base with the negative exponent moved and became positive!

Simplify.

-4 04

1x and y 1

x

6. x-4 y0

You can not have negative or zero exponents in your answer.

4 4

1 1

x

1

x

1. p2

2. p12

3. .

4. .

Simplify -7

-5

p

p

12

1

p

2

1

p

Simplify.

7. 3r4s2

18r3s44 3 2 41

r s6

21rs

6

2

r

6s

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.

8. x 3

x4

7

1

x

Get rid of the negative exponent.

3

4 3 4

x 1

x x x

9. r 5s 2

r3s 3

8

s

r

Get rid of the negative exponents.

Simplify.

5 2 3

3 3 5 3 2

r s s

r s r r s

10. x 3y2 2

4x2 3

x 6y4

43 x6

4

12

y

64x

Get rid of the parentheses.

Simplify.

23 2

32

x y

4x

Get rid of the

negative exponents.

4

3 6 6

y

4 x x

x 6y4

43 x6

1. .

2. .

3. .

4. .

Simplify

22 1

33

-3x

2x

y

y

11

9x

8y

11

-9x

8y

7

-9x

8y

7

9x

8y

ObjectiveThe 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?

23When 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?

9.02The decimal was moved how many places?

8When the original number is less than 1, the

exponent is negative.9.02 x 10-8

Write 28750.9 in scientific notation.

1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 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. 14.28 x 10-4

2. 1.428 x 10-3

3. 14.28 x 1010

4. 1.428 x 1011

Write in PROPER scientific notation.(Notice the number is not between 1 and 10)

4) 234.6 x 109

2.346 x 1011

5) 0.0642 x 104

6.42 x 10 2

Write 531.42 x 105 in scientific notation.

1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108