Dividing Monomials
For all integers “m” and “n” and any nonzero
number “a” ……
m
a
a
n
a
a 1
0
a
n
1
 n
a
When the problems look like
m  n this, and the bases are the
same, you will subtract the
exponents.
ANY number raised to the zero
power is equal to ONE.
If the exponent is negative, it is written
on the wrong side of the fraction bar,
move it to the other side.
1.
f g h
31 21 21
f g h f
fgh
3
3
2 2
2. 24 x y
6 xy
1 1
gh
Subtract the exponents
5
7
2

4 x 2
Divide the coefficients
y
2
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………
24 x3 y 5
2  2  2  3 x  x  x  y  y  y  y  y

7
1  2  3  x  y  y  y  y  y  y  y
6 xy
22 x x
4 x2

  2
1  y  y
y



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.
0 4
5 t wu
2 3 2
t wu
4. 27 x y
4
9 x y
2
2

w2
U’s cancel
Each other
Subtract the exponents
5
6
1t
2

Divide the coefficients
3 x2
y
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.
9
5.
3
x y
6 2
xw u

9

1
6 2 3
x xw u y
1
10 6 2 3
x wu y
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
6.
x
8
x
8
x
 6 
x
Now
Subtract
The
Exponents
x
2
x

1
2
Now divide the coefficients but now ADD the exponents
6
Fix your
negative
exponent
40 x
7.
3
10 x
0
8
4 6
5
x
w
u
8.
xw6u 2

6 3
40x x
10
7
1
u
x

ANY number
raised to the
zero power is
equal to ONE.
w
2
4
9
9
4
x
 1  4x
Now divide the coefficients and combine the exponents
Fix your
negative
exponents
10
2 16
30
x
y
z
9.
5 6 4
5x y z


30 x y z z
10 6
5x y
20
6 z
5 4
x y
5 2 16 4
10.
b 
 3
c 
4
20
b
 15
c
5
Exponents OUTSIDE
And INSIDE …… Distribute!!
11.
v 
 6
w 
9
2
3

6
v
4
w
First – Simplify the numerator!!
2
6
5
( x y )( x y )
12.
8
3
( x y)
Then the
denominator

7
7
x y
24 3
x y
Now
Subtract
The
Exponents

y
4
17
x
First – Simplify the numerator!!
2
8
4
6
9
( x y )( x y )
x
y
13.

9
2
18 2
( x y)
x y
Then the
denominator
Now
Subtract
The
Exponents

y
7
12
x
5 4 0



7
a
b
c
14.

4 3 3 
 5a b c 
Exponents OUTSIDE
And INSIDE …… Distribute!!
4
Fix your
Negative exponents


(7)4 a 20b 16 c0
4
5 a
16
4
12
b
12
5 c
4 4
4
7 a b
c
12
4
16
12
0
12
a b c c
5
 (7)4 20 16
a b
Now
Subtract
The
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)

4 3 0



4
a
b
c
15.

2 2 4 
 3a b c 
Exponents OUTSIDE
And INSIDE …… Distribute!!
6
Fix your
Negative exponents


(4)6 a 24b 18 c0
6
3 a
6
12
24
b
12
3 c
12 6
6
4 a b
c
24
6
12
12
0
a b c c
3
 (4)6a 24 18
b
24
Now
Subtract
The
Exponents
3
5
4 2
16. (4 x y )
5 1 5 4
(4 x y )

20

20
4 y
6 10 4 8
4x xy
6 10
y 8
4 x
20 4 20
4 x y

14
12
4 y
14
x
3
17.
7
6 3
(2 x y )
4 1 7 5
(2 x y )

20

35
2 y
9 21 5 18
2x xy
9 21 18
2 x y
20 5 35
2 x y

17
11
2 y
x
26
1
5 15
18) (125 )
Multiply exponents
= 125
1
3
 125
3
=5
Exponents OUTSIDE
And INSIDE …… Distribute!!
7 2
19) (4 x y )
3
 (4) x y
2
Use ( ) when
Typing the -4
Into calculator!
6
14
16x
 14
y
6
Any neg.
number
raised
to an
even power
is positive