Unit 3: 5.2 Properties of Exponents and Power Functions Day 1
In this lesson you will
(1) Review the properties of exponents
Vocabulary
Base
Exponent
Expanded Form
Name of Property
Product Property
Quotient Property
Definition of Negative
Exponents
Zero Exponents
Power of a Power
Power of a Product
Power of a Quotient
Symbolic Representation
Example
Investigation: Properties of Exponents
Use expanded form to review and generalize the properties of exponents.
Step 1
a.
Write each product in expanded form, and then rewrite it in exponential form.
23  2 4
b. x 5  x 12
c. 10 2  10 5
Generalize your results from Step 1. a m  a n  ?_
Step 2
Step 3
Write the numerator and denominator of each quotient in expanded form. Reduce by eliminating
common factors, and then rewrite the factors that remain in exponential form.
a.
45
42
b.
x5
x6
am
Step 4: Generalize your results from Step 3. n  ?_
a
Step 5
a.
Write each quotient in expanded form, reduce, and rewrite in exponential form.
23
24
b.
45
47
c.
x3
x8
Step 6
Rewrite each quotient in Step 5 using the property you discovered in Step 4.
Step 7
Generalize your results from Steps 5 and y.
1
 ?_
an
Step 8
Write several expressions in the form (an)m. Expand each expression, and then rewrite it in exponential
form. Generalize your results.
Step 9
Write several expressions in the form (a  b) n . Don’t multiply a times b. Expand each expression, and
then rewrite it in exponential form. Generalize your results.
Step 10
Show that a0 = 1, using the properties you have discovered. Write at least two exponential expressions
to support your explanation.
5.2 Exercises to Practice What You Learned
1.
Rewrite each expression as a fraction without exponents or as an integer. Verify that your answer is equivalent
to the original expression by evaluating each on your calculator.
a.
2.
c. -3
-4
d. (-12)
3
e.  
4
-2
2
2
f.  
7
1
a a
8
b6
b. 2
b
3
d0
d. 3
e
4 5
c. (c )
State whether each equation is true or false. If it is false, explain why.
a.
4.
b. -6
2
Rewrite each expression in the form an.
a.
3.
5
-3
3  4  12
5
2
7
x
b. 100(1.06) = (106)
Rewrite each expression in the form axn.
a.
x6  x6
72 x 7
d.
6x 2
b. 4 x 6  2 x 6
 6x5
e. 
 3x
6.6  1012
d.
 7.5  1015
4
8.8  10
4x
c.
 1x
4
x



3


c.  5x 3   2 x 4
 20 x 7
f. 
 4x



2

Name: ___________________________________
Algebra II
Homework 5.2 Part 1 - Properties of Exponents
1.
Rewrite each expression as a fraction without exponents or as an integer. Using your calculator, verify that
your answer is equivalent to the original expression.
a. 3-2
b. 7-3
c. -4-4
d. (-5)
3
e. –  
5
-3
2.
Rewrite each expression in the form xn or axn.
a.
4x  9x
0
8
 88 x 10
d.
 8x 3
3.

b. 8 x
6
2
 15x 
  35 x 7
e. 
2
  7x
14



3
Solve this equation for y. Then carefully graph it on your paper.
y3
 ( x  4) 2
2
 5
f.   
 6
2
x9
c. 9
x
 40 x 8
f. 
2
  8x



3
Exit Ticket
5. You’ve seen that the power of a product property allows you to rewrite a  b  as a n  b n . Is there a power of a
sum property that allows you to rewrite (a + b)n as an + bn? Write some numerical expressions in the form (a +
b)n and evaluate them. Are your answers equivalent to an + bn always, sometimes, or never? Write a short
paragraph that summarizes your findings.
n
Do Now
Write the following in expanded form
3x 
2 4
7 xy
3