Dividing Monomials

For all integers “m ” and “n” and any nonzero number “a” ……m

n

a

am na

When the problems look like this, and the bases are the same, you will subtract the exponents.

0 1a ANY number raised to the zero power is equal to ONE.

na 1na

If the exponent is negative, it is written on the wrong side of the fraction bar, move it to the other side.

1.

3 2 2f g h

fgh

3 1 2 1 2 1f g h 2 1 1f g h

2.

3 5

7

24

6

x y

xy

Div

ide th

e co

effi

cients

Subtract the exponents

4 2x2y

When dividing the coefficients or subtracting the exponents, place the answer on the side of the fraction bar that has the larger value for that term.

If you’re having trouble with the rules, try it like this………

First, factor numerator and denominator into prime factors.

Second, cross out like terms from top to bottom. (reduce) Third, list remaining terms and multiply them back

together.

3 5

7

24

6

x y

xy2 2 2 3

1 2 3

x x x y y y y y

x y y y y y y y

2 2

1

x x

y y

2

2

4

x

y

3.

0 4 2

2 3 2

5 t wu

t w u

1

4.

4 5

2 6

27

9

x y

x y

Div

ide th

e co

effi

cients

Subtract the exponents

3 2xy

When dividing the coefficients or subtracting the exponents, place the answer on the side of the fraction bar that has the larger value for that term.

U’s cancelEach other

2t2w

5. 9 3

6 2

x y

xw u

Remember, if the exponent is negative, the term is written on the wrong side of the fraction bar, move it to the other side.

6 2xw u9x 3y1 1

10x 6 2 3w u y

6. 6

8

x

x

6x

8x

NowSubtract

TheExponents

2x

12x

7. 6

3

40

10

x

x Fix your

negative exponent

640x

10

3x

Now divide the coefficients but now ADD the exponents

4 9x1 94x

8. 0 8 4 6

6 2

5 x w u

xw u

ANY number raised to the zero power is equal to ONE.

1 7x2w

4u

9.

10 2 16

5 6 4

30

5

x y z

x y z

Fix your negative

exponents30

5

5x10x

2 16y z6y

4z

Now divide the coefficients and combine the exponents

65x 4y

20z

10.

54

3

b

c

Exponents OUTSIDEAnd INSIDE …… Distribute!!

20

15

b

c

11.

29 3

6

v

w

6v 4w

2 6 5

8 3

( )( )

( )

x y x y

x y12.

First – Simplify the numerator!!

7x 7y

Then thedenominator

24x 3yNow

SubtractThe

Exponents

4y

17x

2 8 4

9 2

( )( )

( )

x y x y

x y13.

First – Simplify the numerator!!

6x 9y

Then thedenominator

18x 2yNow

SubtractThe

Exponents

7y

12x

14.

45 4 0

4 3 3

7

5

a b c

a b c

Exponents OUTSIDEAnd INSIDE …… Distribute!!

4( 7) 20a 16b 0c

45 16a 12b 12c

Fix yourNegative exponents

4( 7)

4520a

16a16b

12b 12c0c

4547 4a 4b

12cNow

SubtractThe

Exponents

Steps

Multiply exponents Fix negative exponents Any neg. number raised to even power

becomes positive… Subtract exponents (unless they are

beside one another—then add)

15.

64 3 0

2 2 4

4

3

a b c

a b c

Exponents OUTSIDEAnd INSIDE …… Distribute!!

6( 4) 24a 18b 0c

63 12a 12b 24c

Fix yourNegative exponents

6( 4)

6324a

12a18b

12b 24c0c

6364 12a 6b

24cNow

SubtractThe

Exponents

16.

3 5 4 2

5 1 5 4

(4 )

(4 )

x y

x y

64 10x 8y

204 4x 20y

64

20410x 4x 8y

20y 144

14x

12y

17.

3 7 6 3

4 1 7 5

(2 )

(2 )

x y

x y

92 21x 18y

202 5x 35y

92

20221x 5x 18y

35y 112

26x

17y

15 1518) (125 )

Multiply exponents

1

3 = 125

= 5

3 125

3 7 219) ( 4 )x y

2 6 14( 4) x y

6

14

16x

y

Any neg. number raised to an

even poweris positive

Exponents OUTSIDEAnd INSIDE …… Distribute!!

Use ( ) when Typing the -4

Into calculator!