The Laws of Exponents

Exponential Form:

base

exponent

Laws of Exponents:1.Multiplying

2.Dividing

3.Power to a Power

4.Zero Power

5.Negative Exponents

1. Multiplying Exponents

32 × 33 =(43)(44) = 65 · 6 =

Now try these:

(85)(32) =

23 × 32 =

Multiplying ExponentsWhat “law” or rule can you come up with for what happens when we multiply exponents?

Multiplying Exponents Law: If you are multiplying

exponents with the same base, KEEP the BASE & ADD the EXPONENTS!

m n m nx x x

512

2222 93636

So, I get it! When you multiply Powers, you add the exponents!

2. Dividing Exponents(Quotient of Powers Law)

46

43=

89

82=

35 ÷ 34 =

Now try these:56

33=

106

23=

Dividing ExponentsWhat “law” or rule can you come up with for what happens when we divide exponents?

2. Dividing Exponents Law: When dividing exponents with

the same base, KEEP the BASE & SUBTRACT the EXPONENTS!

mm n m n

n

xx x x

x

16

222

2 426

2

6

So, I get it! When you divide Powers, you subtract the exponents!

Now let’s take a look at Brain Pop and then take the quiz to see if you’re

understanding multiplying and

dividing exponents!

3. Raising a Power to a Power

(23)3 =

(54)2 =

(162)3

Power to a PowerWhat “law” or rule can you come up with for what happens when we raise a power to a power?

3. Power to a Power: If you are raising a Power to a power, you

multiply the exponents!

n

m mnx x

52323 55)5(

So, when I take a Power to a power, I multiply the exponents

4. Zero Power46

46=

89

89=

35 ÷ 35 =

4. Zero Law of Exponents: Any base powered by zero

exponent equals one.

0 1x

1)5(

1

15

0

0

0

a

and

a

and

So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.

Negative Exponents:

http://www.virtualnerd.com/pre-algebra/factors-fractions-exponents/exponent-properties/negative-zero-exponents/negative-exponent-definition

5. Negative Exponents: If the base is powered

by the negative exponent, then the base becomes reciprocal with thepositive exponent.

1m

mx

x

933

1

125

1

5

15

2

2

3

3

and

So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha!If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!