Let’s Divide!

Dividing MonomialsChapter 8.3

Quotients of Powers

• How do I find ?

a*a*a*a*a*a = a*a*a*a

a2

1 = a2

6

4

a

a

a*a*a*a*a*a = a*a*a*a

Let’s find a different way

6

4

a

a

In the previous slide, you saw that the result of this fraction was a2.

How do 6 and 4 relate to two?

Quotient of Powers Property

For all non-zero numbers, subtract the exponent of the denominator from the numerator when the bases are the same.

45-2 = 43

5

2

4

4

Let’s prove it.

45-2 = 43 5

2

4 102464

4 16

4 4 4 64

Try Some.

10

5

2?

2

10

7

3?

3

8

3

5?

5

3

2

2?

2

Solutions

210-5 = 25

310-7 = 33

58-3 = 55

23-2 = 21=2

3

2

28 4 2

2

Try Some with variables.

xj-1

xa+b-c

xm+1-1 = xm

?jx

x

?a b

c

x

x

1

?mx

x

Fun Fun Fun

2 5

3

4?

2

x y

xy

4 2

5

48?

1.2

a b

ac

Fun Fun Fun

-2x2-1y5-3=-2xy2

-40a4-1b2c-5

=-40a3b2

c5

2 5

3

4?

2

x y

xy

4 2

5

48?

1.2

a b

ac

Remember negative exponents?

Any time you have a negative exponent, it must be placed in the denominator.

C -3 =3

1

c

Try Some

45 32 1133

answers4

4

1 15

5 625

33

1 12

2 8

1 1133

133

Combine yesterday’s work and today’s

3 235

( )a b

a

32( )3

Combine yesterday’s work and today’s

3 23 2 2 3 6 65

( ) (5 ) 125a b

a b a ba

33

3

2 2 8( )3 3 27

Thanks for enjoying math!