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Unit 6
Exponents and
Radicals
Essential Question:
How do you evaluate expressions
involving rational exponents?
5 minute check
on Unit 5.
Do the first 5 problems!
Over Lesson 7–2
A. 49
B.
C.
D.
Over Lesson 7–2
A.
B. 2n4
C.
D.
Over Lesson 7–2
A.
B.
C.
D.
Over Lesson 7–2
A.
B.
C.
D.
Over Lesson 7–2
A.
B.
C.
D.
You used the laws of exponents to find
products and quotients of monomials.
• Evaluate and rewrite expressions involving
rational exponents.
• Solve equations involving expressions with
rational exponents.
EQ: How do evaluate expressions involving
rational exponents?
• rational exponent
• radical
• cube root
• nth root
• exponential equation
What is a rational number?
A rational number is any number that can be
expressed as the quotient or fraction
p
q
of two integers, with the denominator not equal
to zero.
What is a RADICAL?
If n is a positive integer that is greater than 1 and
a is a real number then,
n
a
where n is called the index, a is called the radicand,
and the symbol √ is called the radical.
Square Root - easy definition
A number that when multiplied by itself equals
a given number.
Root
A number that, when multiplied by itself some
number of times, equals a given number.
n
a
2
a
a
Perfect Squares
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
Perfect Cubes
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
103 = 1000
113 = 1,331
123 = 1,728
1
2
b = b
Square Root
Radical and Exponential Forms
Write each expression in radical form, or write each
radical in exponential form.
=9
Answer: 9
Simplify.
Radical and Exponential Forms
Write each expression in radical form, or write each
radical in exponential form.
Answer:
Radical and Exponential Forms
Write each expression in radical form, or write each
radical in exponential form.
Answer:
Radical and Exponential Forms
Write each expression in radical form, or write each
radical in exponential form.
Answer: 9
A. 16
B. 8
C. 4
D. 2
Write each expression in radical form.
121
1
2
8x
1
2
1
2 2
(36y )
Write each radical in exponential form.
37
17x
5xyz
Assignment: Do Worksheet
#1 to #9
EQ: How do you evaluate
expressions involving rational
If a = b , then b = a.
n
n
nth Roots
A.
Answer: 4
nth Roots
B.
Answer: 5
A. 343
B. 81
C. 49
D. 7
Simplify.
3
64
4
10,000
5
32
1
n
b = b
n
1
3
Cube Root
b = b
1
n
3
nth Root
b = b
n
Evaluate b
Expressions
A.
= 11
Answer: 11
Simplify.
Evaluate b
Expressions
B.
=7
Answer: 7
Simplify.
A. 4
B. 8
C. 16
D. 32
Simplify.
125
1
3
625
1
4
128
1
7
Assignment: Do Worksheet
#10 to #18
EQ: How do you evaluate
expressions involving rational
m
n
b =
( )
n
b
m
= b
n
m
Evaluate b Expressions
= (2)2
25 = 32
=4
Simplify.
Answer: 4
Evaluate b Expressions
= (9)5
92 = 81
= 59,049
Simplify.
Answer: 59,049
A. 216
B. 36
C. 18
D. 6
Simplify.
27
2
3
32
2
5
125
2
3
Assignment: Do Worksheet
#19 to #21
EQ: How do you evaluate
expressions involving rational
b =b Û x= y
x
y
Solve Exponential Equations
A. Solve 9
x
= 729.
9x = 729
Original equation
9x = 9 3
Rewrite 729 as 93.
x=3
Power Property of equality
Solve Exponential Equations
B. Solve 16
2x – 1
162x – 1 = 8
(24)2x – 1 = 23
28x – 4 = 23
8x – 4 = 3
8x = 7
= 8.
Original equation
Rewrite 16 as 24 and 8 as 23.
Power of a Power, Distributive
Property
Power Property of Equality
Add 4 to each side.
Divide each side by 8.
Solve 93x + 1 = 274.
A.
B.
C.
D. 2
Solve 6x = 216.
Solve each equation.
Solve
25x - 1 = 5.
Assignment: Complete the
Worksheet
EQ: How do you evaluate
expressions involving rational