Integer Exponents Day 1

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

ma 322 2 2 2 3 2 2 2

Example 1

3 3 9

9

2(3)

5

Example 2

3 3 9

9

2( 3)

6

Example 3

9

23

Solve:

Laws of Exponentshttps://www.youtube.com/watch?v=QIZTruxt2rQ

Any number raised to the first power is …

31 = 871 =

5289211 = Rule:

Any number raised to the first power is itself. (a1 = a)

Any number raised to the power of zero is ONE!

30 = 870 =

5289210 =

Rule: a0 = 1

Negative Power Property

Saying goes: NO NEGATIVE POWERS

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

3a

Negative Power Property

( ) 1nn

aa

( )aa

33

1

3( )a

Negative Power Property

( ) 1nn

aa

n na bb a

Practice

1) (-4)2

2) 73

3) -54

4) 101

5) 95

6) (-2)0

7) (-2)-1

8) 0-3

9) 3-4

10) (¼)0

Product Rule

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

Product of a Powerm n m na a a

4 5 4 52 2 2 92

512

4 52 2

Product of a Powerm n m na a a

4 5 4 52 2 2 92

512

4 52 2

4 52 2

2

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

Quotient Power Property

m

m nn

aa

a

8

8 33

xx

x

8

3

x

x 5x

Quotient Power Property

mm n

n

aa

a

3

8

x

x

5

1

x

=

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

Power of a Power( ) m n m na a

32 63 3

63

729

323

Power of a Power( ) m n m na a

232

64

( ) 3 22

1

64

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

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?

Properties of ExponentsNegative Power Property:

Product of a Power:

Power of a Power:

Quotient Power Property:

m n m na a a

( ) m n m na a

( ) 1nn

aa

m

m nn

aa

a

Do Now – December 6th

NO CALCULATOR

1. Solve: 0.2x = 7 - 0.8x 2. 6-3

3. -40

4. (-8)2

5. -34