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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