Algebra 2
Unit 6
Ui
Quiz Review
Name:________________________
Unit 6 Quiz Review Days 1-4
Date:___________
Block:______
Simplify Completely. Leave no negative exponents.
8
6
1. (𝑧 )( 𝑧 )
4.
𝑦8
𝑧4
∙
𝑧 10
14.
(5𝑎8 )(6𝑎11 )
24𝑎19
3 2
5. (5𝑘 𝑎 ) (8𝑘 𝑎 )
8. (−2)5
15𝑟 6 2
)
25𝑟 8
3. (7𝑘 6 𝑚4 )2
40𝑚7 𝑦
6 7
𝑦 11
7. −25
11. (
2.
16𝑚3 𝑦 5
6.
9. −62
12𝑐 10
9𝑑 6
÷
20𝑐 7
15𝑑 4
−18𝑟𝑦 7
10. (−6)2
12. (4𝑧 7 ) (2𝑧 4 )3
15.
−45𝑦6 𝑟 3
13.
16.
12𝑐 4 𝑦 6
20𝑐 2 𝑦 8
24𝑥 9
(3𝑥 6 )3
∙
10𝑐𝑦 3
3𝑐 2 𝑦 2
*Rule: exponent inside radical must be smaller than the index
**Recall: You must use absolute value bars around an odd exponent answer of an even index!
Simplify:
17.
4
32
20.
3
 64 y
23.
5
8
18.
3
21.
4
x2 y6
19. 3 y 52
8 9
16ab c
5a 5b 9 c13
22.
24.
4
x4
y8
225 x 2 y10 z 5
Recall: exponent of the radicand goes in the numerator of the rational exponent and the index goes in the
denominator of the rational exponent
Write each expression in exponential form.
25.
3
4
26.
4
73
27.
4
212
28.
5
a 9b15
Write each expression in radical form.
29. 3 0.5
1
30. 5
3
31. 5 4 3 4

3
5
32. 4m  15
2
Properties of Radicals
n
a  n b  n ab
n
a n a

b
b
n
*Product Property: index must be the same
*Quotient Property: index must be the same
Take note: If the index is not the same, you must apply your exponent rules!
Simplify each expression. Assume all variables are positive.
4
4  3 16
34.
35. 64 27 x  24 3x 3
36.
33.
3
162
2
4
3
3
625 xy6
5x 7 y 2
Review: Properties of Exponents:
b m  b n  b m n
(b m ) n  b mn
(ab) m  a m b m
m
am
a
   m
b
b
b
m
1
 m
b
b0  1
bm
 b mn
n
b
Simplify each expression. Assume all variables are positive.
37. (9u 2 v10 )
1
2
38. 5
1
1
39. (8 2  5 3 ) 2
41.
2
1
4




1
4
3
1
 1000a 9 c 8  3

44. 
3 4 
343
b
c


 
1
4
5
 18 14
42.  1
9 4

3
43. 2x 3
2
40. (2 4  3 4 )
71
7
1
0
1
4
1
4
45. 3  3  3  3
1
4
1
2
46. 5  45
1
2
When Adding and Subtracting radicals: simplify each term and look to see if you can combine
like terms. Remember the radical stays the same when you add or subtract the coefficients of the radicals.
Simplify each expression.
47.
75  4 18  5 3

49. 2 6 5 2  4 3
51.
 11  3 7 
2

48. 33 16  43 54  3 128
50.
52.
Find the area and perimeter of the rectangle below.
53.

6 2 5
2 3
1 5

6 2 5

Graphing Radical Functions: