Dividing Monomials
Dividing Powers – Review: Expand and simplify
problems 1-3 as shown in the example. Then answer
questions 4 - 5. (This is a review of what you discovered in Day 7.)
x 5 xixixixix
= x2
Example: 3 =
x
xixix
b8
1) 5 =
b
m4
=
2)
m
3) When I divide a power by a power with the same bases, the __________
stays the same and I ___________________ the exponents.
b8
4) Explain why 5 cannot be simplified.
c
Dividing a Monomial by a Monomial: Answer question 5 and then
expand and simplify problems 6-8 as shown by the given example. Then
answer questions 9-11.
Example:
a 4 b aiai a i a i b a 2
=
=
a 2b 2
a i a i b ib
b
5) Why are we able to “cancel” two “a”s and one “b” in the example?
a6b 4
6) 3 2 =
ab
Intervention Units: Exponents 8.3
x 2 y5 z 3
7) 2 2 =
x y z
1
4 4 i3 4
8) 2 3 =
4 i3
9) Does the rule of “when I divide a monomial by a by a monomial, I
subtract the exponents” apply to questions 6-8 as well? Why or why not?
⎛
a4b6
4−1 6−3
3 3⎞
⎜⎝ For example, ab 3 = a b = a b ⎟⎠
Practice Time: Use the rule you discovered above to simplify the following
monomials. You may leave your answers with negative exponents. (Do
not expand, unless you need to – remember “if in doubt, write it out!”)
a 4 b 4 c3
=
10)
ab 3 c 2
x 2 y4 z
11) 3 4 =
x yz
23 i35
12) 2 3 =
2 i3
m4 n4
13) −2 6 =
m n
4x 5 y
14)
=
8x 2 y 4
15) Rewrite #13 without a negative
exponent.
Intervention Units: Exponents 8.3
2