MODULE 1
EXPONENTIAL NOTATION &
PROPERTIES OF INTEGER
EXPONENTS
Lesson 3
Writing Equivalent Exponential Expressions
Warm Up
1 minute
Find another way to show each of the following:
a)
6
b)
10
c)
15
Learning Target

I can write equivalent expressions using prime
bases.
Pair
Materials – none
2 minutes
Suppose you were given the following:
158 ∙ 36 ∙ 26
102 ∙ 63
Brainstorm with your partner ways that this
problem might be simplified.
Independent
Materials – notes
2 minutes
Let’s start by breaking down the problem.
158 ∙36 ∙26
102 ∙63
(5∙3)8 ∙36 ∙26
(5∙2)2 ∙(3∙2)3
Step 1:
Factor
each base
into prime
factors
Do you notice common bases?
Independent/Pair
Materials – notes
2 minutes
Let’s break it down even more:
(5 ∙ 3)8 ∙ 36 ∙ 26
(5 ∙ 2)2 ∙ (3 ∙ 2)3
58 ∙ 38 ∙ 36 ∙ 26
52 ∙ 22 ∙ 33 ∙ 23
Step 2:
Share the
exponent
with its
factors
How can you simplify? Share with your
partner your thoughts.
Independent/Pair
Materials – notes
2 minutes
58 ∙ 38 ∙ 36 ∙ 26
52 ∙ 22 ∙ 33 ∙ 23
Because the base 2’s AND the
base 3’s are being Multiplied, we
need to Add the exponents for
each base
Step 3: Use
MADSEEM!
58 ∙ 314 ∙ 26
52 ∙ 25 ∙ 33
Now what? Share with your partner.
Independent
Materials – notes
2 minutes
58 ∙ 314 ∙ 26
52 ∙ 33 ∙ 25
Because the base 5’s AND the
base 3’s AND the base 2’s are
being Divided, we need to
Subtract the exponents for each
base.
56 ∙ 311 ∙ 21
Step 3: (Still)
Use
MADSEEM!
Independent
Materials – none
1 minute
56 ∙ 311 ∙ 21
I can write equivalent expressions using
prime bases.
 Is this equal to the original problem? (let’s check on a calculator!)
 Are the bases prime?
5?
3?
2? YES!
Individual/Partner
Materials – white board or scratch paper
5 minutes

Now try on your own!
Write an equivalent expression using prime bases
55 ∙ 68
102
Exit Ticket!
4 minutes
On the half piece of scratch paper that was
handed out to you,
1) Write your name

2) Write an equivalent expression using prime bases:
95 ∙ 2 8
32 ∙ 6 3
Learning Target Debrief
I can write equivalent expressions using prime
bases.





5- I can teach it!
4- I feel really good about it!
3- I’m starting to get it!
2- I’m still struggling a lot with it and might need
some extra help
1- I have no idea where to start, and I definitely
need some help!