Download The Product Rule and Power Rules for Exponents

Elementary Algebra
Section 5.1
Page 1 of 2
Section 5.1: The Product and Power Rules for Exponents
Big Idea: There are shortcut formulas to doing calculations with exponents.
Rules for Exponents:
For positive integers m and n:
Rule Name
Product Rule
Rule
a m  a n  a mn
a 
 a mn
3 
 ab 
 a mb m
2 p
m n
Power Rules
Example
6 2  6 4  6 2  4  66
m
m
am
a

 
bm
b
2 4
5
 32(4)  38
 25 p 5
2
2
5 5

 
2
 3 3
1. Product Rule Activities:
a. Calculate 8  16 =
b. Now re-write the problem with every number written using exponents:
c. Calculate 81  729 =
d. Now re-write the problem with every number written using exponents:
e. What is the pattern?
f. Make your own statement of the Product Rule:
g. Calculate 25  625 using the Product Rule:
h. Calculate 60  48 =
i. Now re-write the problem with every number written in prime factorized form using exponents:
j. Calculate 120  360 using the Product Rule:
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra
Section 5.1
Page 2 of 2
2. Power Rule #1 Activities
a. Calculate 813 =
b. Now re-write the problem with every number written using exponents:
c. Calculate 164 using the Power Rule #1:
3. Power Rule #2 Activities
a. Calculate 362 =
b. Now re-write the problem with every number written using exponents:
c. Calculate 603 using the Power Rule #2:
4. Power Rule #3 Activities
3
 4
a. Calculate   
7
b. Now re-write the problem with every number written using exponents:
2
 16 
c. Calculate   using the Power Rule #3:
 25 
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.