Algebra II Review 6.1-6.2 ANSWER KEY
Algebra II Review 6.1-6.2 ANSWER KEY
6.1 Evaluate Nth Roots and use Rational Exponents
Things you should be able to do: - Rewrite radical expressions using rational exponent notation - Rewrite rational exponent expressions using radical notation - Evaluate an Nth root without using a calculator - Solve an equation using Nth roots
Examples:
Rewrite the radical expression using rational exponent notation:
1. 3 7 = 71 3
( ) ( ) 2.
36
2
=
61 3
2 = 62 3
( ) ( ) 3.
9 -2
4
=
(-2)1 9
4 = (-2)4 9
Rewrite the rational exponent expression using radical notation.
1
4. 173 = 3 17
( ) ( ) 3
5. 47 =
41 7 3 =
3
74
( ) ( ) 7
6. (-28)5 =
(-28)1 5
7
=
7
5 -28
Evaluate the expression using Nth roots without using a calculator.
( ) 7. 3 8 2 = (2)2 = 4
( ) 8. 4 81 3 = (3)3 = 27
( ) 3
9. 362 =
36 3 = (6)3 = 216
( ) 4
10. 1253 =
3 125 4 = (5)4 = 625
1
11. (-8)3 = 3 -8 = -2
( ) ( ) 5
12. (-27)3 =
(-27)1 3 5 =
3 -27 5 = (-3)5 = -243
Solve an equation using Nth roots. (Round decimals to two places)
x3 +17 = 132
13.
x3 = 115
x = 3 115
x 4.86
2x5 + 73 = 53
2x5 = -20
14.
x5 = -10
x = 5 -10
x -1.58
( x + 3)4 = 362
x + 3 = ? 4 362
15.
x = ? 4 362 - 3
x 1.36
x -7.36
3(2x -1)4 = 111 (2x -1)4 = 37
16. 2x -1 = ? 4 37 2x = ? 4 37 +1 x = ? 4 37 +1 2 x 1.73 x -.73
5 - (3x + 2)3 = 15
- (3x + 2)3 = 10
(3x + 2)3 = -10
17.
3x + 2 = 3 -10
3x = 3 -10 - 2
x = 3 -10 - 2 3
x -1.38
6.2 Apply Properties of Rational Exponents
Things you should be able to do: - Simplify expressions using your properties of rational exponents - Simplify radical expressions using properties of radicals
Simplify the following expressions using your properties of rational exponents. Leave
your answer as a rational exponent if necessary.
( ) 1.
32 3
12
21
= 33 2
2
= 36
1
= 33
12
2
2
( ) 2. 8x2 1 3 = 83 x 3 = 3 8 x 3 = 2x 3
3.
x2 3 x1 2
=
2-1
x3 2
=
4-3
x6 6
=
1
x6
( )2
4.
64 x
2
3
=
642 3 x2 3
=
3 64 x2 3
=
42 x2 3
=
16 x2 3
( ) 5.
x5 6
-3 = x-15 6 =
1 x15 6
( ) 6.
33 2 33
13
= 33 6 33 3
1 +1
= 32
1+2
= 32 2
3
= 32
7.
52
57
2
-1 3
=
5-2 3 57 2
-2-7
=5 3 2
- 4 - 21
=5 6 6
- 25
=5 6
=
1 525 6
8. 4 4 4 64 = 4 4 64 = 4 256 = 4
(( ) ) 9. 4 3
6 =
61 2
13
1
4
=
61
24
Simplify the following radical expressions. Leave your answer in radical form.
10. 4 3x7 y9 z3 = 4 3x4 x3 y 8 yz3 = xy2 4 3x3 yz3
11. 3 x3 y4 z7 = 3 x3 y3 yz6 z = xyz2 3 yz
12. 24x5 y8 z3 = 4 6x4 xy8 z2 z = 2x2 y4 z 6xz
13. 5 3a10b17c29 = 5 3a10b15b2c25c4 = a2b3c5 5 3b2c4
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