Warm UpWarm Up

3

2

2

3. 2

4. 4

5. 4

1. 3x2 + 2x + 3

2. –x4 + 3x3 – 3x + 4

3. 8

4. 16

5. -16

Add or subtract the following polynomials

2 2

4 4 3

1. 2 5 3 2

2. 2 4 2 3

x x x x

x x x x x

Solve.

Lesson 10.2 Lesson 10.2 Rules of ExponentsRules of Exponents

Multiplying and powersMultiplying and powers

SWBAT: Simplify expressions involving SWBAT: Simplify expressions involving exponents.exponents.

ReviewReview

Base3x

Exponent or power

The _______ tells you _____________________________________________. The__________________tells you ________________________________________________.

basewhat number or variable you are going to multiply exponent or power

how many times the base is multiplied by itself.

ReviewReviewWhen you are When you are addingadding terms: terms:

only the coefficient (the number in only the coefficient (the number in front) changes.front) changes.

When you are When you are multiplyingmultiplying terms: terms:

the coefficient and the exponent the coefficient and the exponent change.change.

Discovering Rule #1Discovering Rule #1

Simplify each expressionSimplify each expression

What do you notice?What do you notice?

3 2 3 2 3

2 3 2 3 4 3 4 2 7

2 2 3 3 2 3 2

2 3x x x y xy a h a h

32 81 144

5x3 7x y 5 116a h

11stst Rule of Exponents Rule of Exponents

11stst Rule of Exponents Rule of Exponents: : When you multiply powers When you multiply powers with thewith the samesame basebase, you , you mustmust ADDADD the exponents. the exponents. So the rule isSo the rule is

m n m na a a

ExamplesExamples

Ex. 1: Ex. 1:

Ex. 2: Ex. 2:

Ex. 3: Ex. 3:

12 ( )e e

3 37 2a a

3 4 23 3a n a n

13e

614a

5 59a n

Discovering Rule #2Discovering Rule #2

Write each answer with a single exponent.Write each answer with a single exponent.

What do you notice?What do you notice?

3 4 22 3 4x c n

6 12 8x c n

22ndnd Rule of Exponents Rule of Exponents

22ndnd Rule of Exponents: When you have an exponent Rule of Exponents: When you have an exponent raised to another exponent, you must multiply the raised to another exponent, you must multiply the exponents.exponents.

Ex. 4: Ex. 4:

Ex. 5: Ex. 5:

Ex. 6: Ex. 6:

42x

33x

322

nm m na a 8

9

64

x

x

33rdrd Rule of Exponents Rule of Exponents33rdrd Rule of Exponents: Rule of Exponents: When you have aWhen you have a productproduct

raised to a powerraised to a power, , all partsall parts are raised to the are raised to the power.power.

Ex. 7Ex. 7

Ex. 8Ex. 8

Ex. 9Ex. 9

3xy

222x

33 23x y

m m mab a b3 3

9 6

4

27

4

x y

x y

x

You Try:You Try:

1.1. 5. 5.

2.2. 6. 6.

3.3.

4. 4.

443k

326 2 fd

24xy

2 52 (3 )x x

3 2 2 54 3a b a b

3 25 73 2x x

AnswersAnswers16

3 6

2 2

7

5 7

29

1. 81

2. 48

3. 16

4. 6

5. 12

6. 108

k

f d

x y

x

a b

x

Summary/ReflectionSummary/Reflection

How will you remember the first three rules of How will you remember the first three rules of exponents?exponents?

Homework: Worksheet 10.1Homework: Worksheet 10.1