ExponentsExponentsExponentsExponents

Objective #1Objective #1: Students will write : Students will write numbers in exponential form numbers in exponential form

Objective #2Objective #2: Students will multiply : Students will multiply and divide numbers in exponential formand divide numbers in exponential form

Parts of a Power

63

Base: the big number; the number being multiplied

Exponent: the little number; tells how many times to multiply the base

Power: the base and exponent together

The Laws of Exponents

Law #1: Any base raised to the exponent

of 1 is equal to the base. EX: 21 = 2

Law #2: Any base raised to the exponent of 0 is equal to 1.

.EX: 100 = 1

The Laws of Exponents

Law #3: A negative base raised to an even exponent is ALWAYS positive.

EX: (-5)2 = 25

Law #4: A negative base raised to an odd exponent is ALWAYS negative.

.EX: (-5)3 = -125

The Laws of Exponents

Law #5: If a fraction is raised to a power then distribute the exponent to both the top and the bottom.

EX:

Law #6: A base raised to a negative exponent is equal to a fraction.

EX: (5)-3 = 1 = 1 (5)3 125

4 4

4

2 2 16= =

3 3 81

Practice ProblemsSimplify:

1. 2.

3. 4.

5. 6.

1 25 = 05

2(-6) =3(-2) =

-24 = 0(-8) =

25

36

1

-8

1

116

Multiplication of Powers

**You can only multiply powers that have the same base. (EX: 23 and 25)

**To multiply powers of the same base, add their exponents.

EX: 23 • 25 = 23+5 = 28

**If a power is raised to another power, multiply the exponents together.

EX: (23)5 = 23•5 = 215

Division of Powers

**You can only divide powers that have the same base. (EX: )

**To divide powers of the same base, subtract their exponents.

EX:4

4-2 22

3=3 =3

3

4

2

33

Practice ProblemsSimplify:

7. 8.

9. 10.

11. 12.

2 3(2 ) = 3 23 3 =

087 = 2(4 5) =

2(9b) = 3 4(2a ) =

64 81

1 400

81b2 16a1

2