The Quotient Rules
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The Quotient Rules. x a. x a. x a. 1. =. x a – b. if a > b. 1. x a. x b. x b. 2. =. if b > a. 3. =. x 0. = 1. x b – a. The Quotient Rules. x a. =. x a – b. if a > b. 1. x b. 5. Divide. 10 13. a. 10 7. 10 13 – 7. 10 6.

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X b

xa

xa

xa

1

=

xa –b

if a > b

1.

xa

xb

xb

2.

=

if b > a

3.

=

x0

= 1

xb –a


X b

xa

=

xa –b

if a > b

1.

xb


X b

5. Divide.

1013

a.

107

1013 – 7

106

10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

10 • 10 • 10 • 10 • 10 • 10 • 10

Count how many are crossed out.

Just subtract the exponents.


X b

5. Divide.

b.

x11

x

x11 – 1

x10

Higher exponent in numerator.

Subtract the exponents.


X b

5. Divide.

c.

y18

y8

y18 – 8

y10

Higher exponent in numerator.

Subtract the exponents.


X b

xa

xa

1

=

xa –b

if a > b

1.

xb

xb

2.

=

if b > a

xb –a


X b

6. Divide.

c3

a.

1

1

c4

c

c4 – 3

c• c• c

c• c• c• c

The higher exponent is in the denominator.


X b

6. Divide.

b.

1

1031

1

1056 – 31

1056

1025

The higher exponent is in the denominator.


X b

6. Divide.

c.

1

1

z15

z6

z21 – 15

z21

The higher exponent is in the denominator.


X b

7. Divide.

x7

-7

a.

1

-21

x9

3x2

1

3

x9 – 7

Simplify.

The higher exponent is in the denominator.


X b

7. Divide.

x11

15

b.

-3

x4

-5

x11 – 4

1

-5x7

Simplify.

The higher exponent is in the numerator.


X b

7. Divide.

x8

23

c.

1

46

x9

2x

1

2

x9 – 8

Simplify.

The higher exponent is in the denominator.


X b

8. Divide.

x7

y9

a.

y10

x7

y10 – 9

x7

y

Can’t simplify.

The higher exponent is in the denominator.


X b

8. Divide.

y6

12

x5

b.

-24

x3

y8

x5 – 3

-1

2

y8 – 6

-x2

2y2

Simplify.

The higher exponent is in the numerator.

The higher exponent is in the denominator.


X b

xa

xa

xa

1

=

xa –b

if a > b

1.

xa

xb

xb

2.

=

if b > a

3.

=

x0

= 1

xb –a


X b

9. Divide.

a.

= 107– 7

= 100

107

107

1

Same exponent.


X b

9. Divide.

12

a4

b.

15

a4

4

5

Simplify.

Same exponent.


X b

10. Divide.

-20

a3

b8

c4

a.

-5b

a3

b7

c5

28

7c

b8 – 7

-5

7

c5 – 4

Simplify.

Same exponent.

The higher exponent is in the numerator.

The higher exponent is in the denominator.


X b

10. Divide.

5

x0

y6

b.

1

x4

y8

10

2x4y2

1

2

y8– 6

x4

Simplify.

0 exponent.

The higher exponent is in the denominator.


X b

11. Simplify.

(

3

)(

)

a2

b4

-6

a

b5

16a5b7

a3

-18

b9

16

a5

b7

b2

-9

Multiply.

8

a2

Add the exponents in the numerator.

Simplify.

Subtract the exponents.


X b

xa

xa

xa

1

=

xa –b

if a > b

1.

xa

xb

xb

2.

=

if b > a

3.

=

x0

= 1

xb –a


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