Download Chapter 1 Lesson 5 Classwork: Properties of Exponents

Name _______________________________________ Date __________________ Class __________________
Reteach
LESSON
1-5
Properties of Exponents
Write
Read
Expanded Form Exponent Form
aa
a2
a squared
aaa
a3
a cubed
aaaa
a4
a to the fourth power
aaa
an
a to the nth power
4x5  4(x  x  x  x  x)
List the factors to expand
exponential expressions.
(4x5)  (4x)(4x)(4x)(4x)(4x)
(4x)5  (4x)(4x)(4x)(4x)(4x)
4x3(y  6)2  4(x)(x)(x)(y  6)(y  6)
Zero Exponent Property: a0  1; a is not zero
Negative Exponent Property: a
34 
2
5
 
n
1
a
 n and  
a
b
380  1
n
n
b
   ; a is not zero.
a
1
1
1


4
3
3
3
3
81
3
3
3
5 5 5 125
5
  

2
2 2 2
8
 
Write each expression in expanded form.
1. 8c3
8(c  __________)
3. a3(b  c)2
2. (3xy)4
___________________
____________________
Evaluate each expression.
4. 61
________________________
7. (4)
6. 122
5. 100
3
________________________
10. 50
________________________
________________________
 1
8.  
7
2
3
9.  
4
________________________
 2 
11.  
 5 
________________________
2
3
________________________
 1
12.   
3
________________________
2
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
1-38
Holt Algebra 2
Name _______________________________________ Date __________________ Class __________________
LESSON
1-5
Reteach
Properties of Exponents (continued)
Properties of Exponents (m and n are integers; a and b are
nonzero real numbers.)
am
 am n
an
Same Base: am  an  am n
To multiply, add
exponents.
(am)n  am  n
To divide, subtract
exponents.
To raise to a power,
multiply exponents.
Different Bases: (ab)m  ambm
Distribute the exponent.
m
am
a

b
bm
 
Combine properties of exponents to simplify expressions with exponents.
(2x5)4
24(x5)4
24x5  4
24x20
16x20
Distribute the exponent.
Multiply exponents.
c4d(c3d 2)
c4c3dd 2
c43d12
Group like variables.
Add exponents.
Simplify.
cd3
Simplify.
3rs 5
r 4s 3
3r14s53
Subtract exponents.
3r3s2
Simplify.
3s 2
r3
Record answer with positive exponents.
Simplify each expression. Assume all variables are nonzero.
13. (5ab3)2
(5)2a2b3  2
________________________
6s 3 t
16.
3st 2
14. w2x5(w4 x3)
y4y2z3z2
w24x53
________________________
 a4 
17.  2 
b 
15. y4z3(y1z)2
________________________
3
18. 3x2y3(9x1y5)
6 31 12
s t
3
a4
b2
3
________________________
________________________
3(9)x21y35
3
________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt Algebra 2