Review of 8-4 & 8-5
7/29/2017
Problems of the Day
Simplify the expression.
a.
 12x
14
144x
7
b. 3
9n  3n  27n
c.
160x  16 10  x  x
4
17
3
15
10
3
27
12
4
 (2 x ) 10 x
3 4
3
 3n
3
9
Review of 8-5
7/29/2017
Problems of the Day
Simplify the expression.
d. 3
64x
30
1
6
 64 x
30
6
 2x
e. 5
8n  4n  32n
f.
128x  64  2  x  x
6
17
3
5
17
5
20
12
6
 (2 x ) 2 x
2 6
5
5
 2n
5
4
Review of 8-5
7/29/2017
e) Find the geometric mean of the integers from
1 to 10 to nearest hundredth.
10
10
1 2  3  4  5  6  7  8  9 10
3,628,800  3,628,800
1
( )
10
 4.53
Review of 8-6
7/29/2017
Problems of the Day
Rewrite each expression without a radical sign
in the denominator.
a.)
b.)
1
5g
2
11
16 x
1
c.)
2 34
5g

5g
x
 6
2x
3

1
2
Review of 8-6
7/29/2017
Problems of the Day
Rewrite each expression without a radical sign
in the denominator.
a.)
1
5g
5g
1


5g
5g
5g
5g
Review of 8-6
7/29/2017
Problems of the Day
Rewrite each expression without a radical sign
in the denominator.
2
b.)
11
16 x
2
11
16 x

11
16 x
11
16 x
11
2 16 x

11
16 x
2 16  x  x

11
16 x
10
2  4  x x 8x x


11
11
16 x
16 x
5
5
x
 6
2x
Review of 8-6
7/29/2017
Problems of the Day
Rewrite each expression without a radical sign
in the denominator.
c.)
1
2 34

2 34 2 3 4
2 34
2 34
2 34



4 9  8 3  8 3  16 4 9  16
(4  3)  16
2 34 2 34 2 3 4
3







1
4 4
12  16
4
2
8-7 & 8-8
7/29/2017
8-7
Powers and Roots
of Negative Numbers
8-7 & 8-8
7/29/2017
Integer Powers
A negative integer raised to a positive odd
power is a negative number.
A negative integer raised to a positive even
power is a positive number.
A negative integer raised to a negative odd
power is a negative fraction.
A negative integer raised to a negative even
power is a positive fraction.
8-7 & 8-8
7/29/2017
Integer Powers
(4)  64 (2)  16
1
1
3
3
(5)  ( )  
125
5
1 2
1
2
(6)  ( ) 
6
36
3
4
8-7 & 8-8
7/29/2017
Roots of Negatives
When x is negative and n is an odd integer
greater than 2: n x stands for the real nth
root of x.
3
5
8 
 32 
-2
-2
3
3
 27 
 216 
-3
-6
8-7 & 8-8
7/29/2017
Theorem
n
When x and n y are defined and are
real numbers, then
n
xy is also defined
and xy  x  n y .
n
n
8-7 & 8-8
Lesson Review
1. Write (–6)4 • (–6) –5 as a power.
2. Evaluate.
5
a.
5
(2)
b.
8
(4)8
–2
4
3. Simplify.
a.
5
 243
b.
3
 128
–3
3
(4) 2
(–6) –1
7/29/2017
8-7 & 8-8
7/29/2017
8-8
Solving Equations
with Radicals
8-7 & 8-8
7/29/2017
Solving Radical Equations
To Solve an equation where the variable
is inside a radical:
• Get the radical alone on one side.
• Raise both sides of the equation to the
root of the radical.
• Solve for the variable.
• ALWAYS Check your answer!!!!!
8-7 & 8-8
7/29/2017
Solving Radical Equations
(4)3 x  19  27
( 4) 3 x  8
3
x 2
 x   2
3
3
3
x 8
CHECK:
(4)3 8  19  27
42  19  27
C
8-7 & 8-8
7/29/2017
Extraneous Solutions
Sometimes what appear to be solutions
really are not solutions. This is why you
must always check:
CHECK: 3  6 64  5
6
3 x  5
3 2  5
6 x  2
6
x  2
 x
6
6
  2 
x  64
6
D
Solutions that don’t
really work are
called extraneous.
8-7 & 8-8
7/29/2017
Lesson Review
Find all real solutions. Be sure to check for extraneous
solutions.
a)
b)
c)
d)
4
a  3 81
(4) c  4 – 1
5
d  3  5
No Real Solutions
24  (15)5 f  1  6 31
8-7 & 8-8
7/29/2017
Assignment
• Worksheet 8-7 & 8-8 (Front & Back)
• (8-7) Pages 515-516 #'s 2-5, 11-13, 15-17,
22, 23, 25a.
• (8-8) Pages 519-520 #'s 1-4, 8, 9, 15-17.
• Quiz on Sections 8-4 to 8-6 on
Wednesday, May 20th!!!
• Chapter 8 Test on Friday, May 22nd!!!