7/3/2015 11:50 amr.2 - integer exponents1 exponents section r.2

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Exponents

Section R.2

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Definitions

Base: The term/variable of which is being raised upon

Exponent: The term/variable is raised by a term. AKA Power

ma BASEBASE

EXPONENTEXPONENT

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Definitions

ma 322 2 2

2 3 2 2 2

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Definitions

no negative exponents!

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Example 1

3 3 9

9

2(3)

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Example 2

3 3 9

9

2( 3)

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Example 3

9

23

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Example 4

2

1

3

1

9

2(3)

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Example 5

3

23

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Warm-Up Solve:

3

3

3

3

1 41.

2 7

2. 2

3. -2

4. - 2

5. 2

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Properties of ExponentsNegative Power Property:

Product of a Power:

Power of a Power:

Power of a Product:

Quotient Power Property:

m n m na a a ( ) m n m na a

( ) m m mab a b

( ) 1nn

aa

m

m nn

aa

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n na bb a

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Negative Power Property

Saying goes: NO NEGATIVE POWERS

What are the base(s) and the power(s)?

3a

( ) 1nn

aa

n na bb a

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Negative Power Property

( ) 1nn

aa

( )aa

33

1

3( )a

Negative Power Property

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( ) 1nn

aa

n na bb a

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Product of a Power

Saying goes: BASE, BASE, ADD

If the BASES are same, ADD the powers

What are the base(s) and the power(s)?

4 52 2

m n m na a a

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Product of a Powerm n m na a a

4 5 4 52 2 2 92

512

4 52 2

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Product of a Powerm n m na a a

4 5 4 52 2 2 92

512

4 52 2

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Your Turn4 52 2

2

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Power of a Power

Saying goes: POWER, POWER, MULTIPLY

If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES

What are the base(s) and the power(s)? 323

( ) m n m na a

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Power of a Power

( ) m n m na a

32 63 3

63

729

323

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Power of a Power

( ) m n m na a

232

64

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Your Turn

( ) 3 22

1

64

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Power of a Product

Saying goes: DISTRIBUTE THE POWER TO THE BASES

What are the base(s) and the power(s)?

( )43x

( ) m m mab a b

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Power of a Product

( ) m m mab a b

4 4 4(3 ) (3) ( )x x

481 x

x 481

4(3 )x How many

bases does this problem have?

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Power of a Product

( ) m m mab a b

y

x

3

3

x y1 3( )

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Your Turn

( ) m m mab a b

x 664

3 2( 8 )x

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Quotient Power Property

Saying goes: When dividing an expression with a power, SUBTRACT the powers. They must have the same base in order to subtract.

What are the base(s) and the power(s)?

8

3

x

x

m

m nn

aa

a

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Quotient Power Property

mm n

n

aa

a

8

8 33

xx

x

8

3

x

x 5x

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Quotient Power Property

mm n

n

aa

a

3

8

x

x

5

1

x

Your Turn

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=

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Assignment

Pg 27 73-93 odd