TRS 82
Day 25 Activity
Rules of Exponents #1
Using factor tiles to represent monomials and ratios of monomials
Each group will need a set of factor tiles and a fraction bar.
red tile (R): x
yellow tile (Y): y
blue tile (B): z
green tile (G): w
The number tiles are used for prime factors.
First let’s practice representing expressions using the factor tiles and the fraction bar.
Notice that on the fraction line, there is a fixed factor of 1 in both the numerator and the
denominator.
Algebraic Expression
Tiled Expression
x2y3
would be represented as
1RRYYY
1
2xy8
would be represented as
1  2 RYYYYYYYY
1
1
x3
would be represented as
1
1RRR
xy 2
12 z
would be represented as
1RYY
1  2  2  3B
25 xyz
18w 3
would be represented as
1  5  5 RYB
1  2  3  3GGG
Activity 1:
1) Please place your factor tiles on the fraction bar to represent the following:
a)
4x3 y 2
6z 3
b)
8x3y
c)
5
xy 2
d)
xy
9x 2 y 3
e)
1
x
TRS 82
Day 25 Activity
Rules of Exponents #1
Using factor tiles to represent multiplication of monomials
Consider the following product:
(3x2y3) (5x3y4)
Using the factor tiles this product could be modeled as:
1  3RRYYY 5 RRRYYYY
1
A rearrangement of the factor tiles would be
1  3  5 RRRRRYYYYY YY
which is the model for 15x5y7.
1
Activity 2:
1. Use the factor tiles to demonstrate multiplication of monomials.
i. Represent each product on the fraction bar.
ii. Rearrange the tiled expression by putting like tiles together and coefficients
together.
iii. Using the rearranged tiled expression as a guide, write the final answer (in
algebraic form) in the blank.
a) (x2y)(x3)
_____________________________
b) (xy) (x3w)
_____________________________
c) (xy4u3)(x3y2)
_____________________________
d) (x3y)(x2y3z2)
_____________________________
e) (xyz)(xyz)
____________________________
f) (x2y2z2)(xy3z)
____________________________
g) (3x2y)(5x4y)
____________________________
h) (8x2yz)(4xy2)
____________________________
i) (2y4w)(7x4y3)
____________________________
j) (9xy)(4x2y3z)
____________________________
TRS 82
Day 25 Activity
Rules of Exponents #1
2. Summarize in your own words the algebraic procedure for multiplying exponential
expressions. Specifically, what happens with the coefficients? What happens with
the exponents?
______________________________________________________________________
______________________________________________________________________
Using factor tiles to represent division of monomials
6x3 y 4
4 xy 2
1  2  3RRRYYYY
Using the factor tiles this is
. Now, remove any pairs of like tiles that appear in
1  2  2 RYY
both numerator and the denominator. Each pair removed is equivalent to a factor of 1
R
1  3RRYY
( =1, etc.). Now the simplified expression looks like this:
which in algebraic form
2 1
R
3x 2 y 2
3x 2 y 2
6x3 y 4
is
. Hence, you have shown that the expression
simplifies to
.
2
2
4 xy 2
Consider the following ratio:
Activity 3:
1. Use the factor tiles to demonstrate division of monomials.
i. Represent each product on the fraction bar.
ii. Remove pairs of like factors from the numerator and the denominator to simplify
the expression.
iii. Using the simplified tiled expression as a guide, write the simplified expression
(in algebraic form) in the blank.
a)
x4 4
xy 3
__________________
b)
x
x4
__________________
c)
5x 3 y 4
10 x 4 y 5
__________________
d)
8 x 3 yz 4
18 xy5 z 4
__________________
3x 7 y 2
e)
x3 z
___________________
TRS 82
Day 25 Activity
Rules of Exponents #1
2. Summarize the algebraic procedure for dividing exponential expressions. Specifically, what
happens with the exponents? What happens with the coefficients?
______________________________________________________________________________
______________________________________________________________________________
3. (Mixed practice). Use the factor tiles to simplify the following expressions.
a)
( xy 2 z )( x 2 yz 3 )
x3 y
__________________________
b)
( xyz 3 )( x 2 )
( yz 4 )( x 3 z )
___________________________
c)
( x 2 y 2 )( xy)
y3z 2
___________________________
d)
(12 x 2 y )(3x 2 z )
18 x 4 yz 2
___________________________
e)
(2 x 5 yz 2 )( x 2 z )
4 x 4 yz 2
___________________________
( x 5 yz 2 )( x 2 z )
f)
x 6 yz 3
___________________________