17.4E: Exercises
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- Aug 13, 2020
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Practice Makes Perfect
Exercise SET A: simplify expressions with a1n
In the following exercises, write as a radical expression.
- a. x12 b. y13 c. z14
- a. r12 b. s13 c. t14
- a. u15 b. v19 c. w120
- a. g17 b. h15 c. j125
- Answer
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1. a. √x b. 3√y c. 4√z
3. a. 5√u b. 9√v c. 20√w
Exercise Set B: simplify expressions with a1n
In the following exercises, write with a rational exponent.
- a. 7√x b. 9√y c. 5√f
- a. 8√4 b. 10√s c. 4√t
- a. 3√7c b. 7√12d c. 24√6b
- a. 4√5x b. 8√9y c. 75√3z
- a. √21p b. 4√8q c. 46√36r
- a. 3√25a b. √3b c. 8√40c
- Answer
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1. a. x17 b. y19 c. f15
3. a. (7c)14 b. (12d)17 c. 2(6b)14
5. a. (21p)12 b. (8q)14 c. 4(36r)16
Exercise SET C: simplify expressions with a1n
In the following exercises, simplify.
- a. 8112 b. 12513 c. 6412
- a. 62514 b. 24315 c. 3215
- a. 1614 b. 1612 c. 62514
- a. 6413 b. 3215 c. 8114
- a. (−216)13 b. −21613 c. (216)−13
- a. (−1000)13 b. −100013 c. (1000)−13
- a. (−81)14 b. −8114 c. (81)−14
- a. (−49)12 b. −4912 c. (49)−12
- a. (−36)12 b. −3612 c. (36)−12
- a. (−16)14 b. −1614 c. 16−14
- a. (−100)12 b. −10012 c. (100)−12
- a. (−32)15 b. (243)−15 c. −12513
- Answer
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1. a. 9 b. 5 c. 8
3. a. 2 b. 4 c. 5
5. a. −6 b. −6 c. 16
7. a. not real b. −3 c. 13
9. a. not real b. −6 c. 16
11. a. not real b. −10 c. 110
Exercise SET D: simplify expressions with amn
In the following exercises, write with a rational exponent.
- a. √m5 b. (3√3y)7 c. 5√(4x5y)3
- a. 4√r7 b. (5√2pq)3 c. 4√(12m7n)3
- a. 5√u2 b. (3√6x)5 c. 4√(18a5b)7
- a. 3√a b. (4√21v)3 c. 4√(2xy5z)2
- Answer
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1. a. m52 b. (3y)73 c. (4x5y)35
3. a. u25 b. (6x)53 c. (18a5b)74
Exercise SET E: simplify expressions with amn
In the following exercises, simplify.
- a. 6452 b. 81−32 c. (−27)23
- a. 2532 b. 9−32 c. (−64)23
- a. 3225 b. 27−23 c. (−25)12
- a. 10032 b. 49−52 c. (−100)32
- a. −932 b. −9−32 c. (−9)32
- a. −6432 b. −64−32 c. (−64)32
- Answer
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1. a. 32,768 b. 1729 c. 9
3. a. 4 b. 19 c. not real
5. a. −27 b. −127 c. not real
Exercise SET F: use the laws of exponents to simplify expressions with rational exponents
In the following exercises, simplify. Assume all variables are positive.
- a. c14⋅c58 b. (p12)34 c. r45r95
- a. 652⋅612 b. (b15)35 c. w27w97
- a. y12⋅y34 b. (x12)23 c. m58m138
- a. q23⋅q56 b. (h6)43 c. n35n85
- a. (27q32)43 b. (a13b23)32
- a. (64s37)16 b. (m43n12)34
- a. (16u13)34 b. (4p13q12)32
- a. (625n83)34 b. (9x25y35)52
- a. r52⋅r−12r−32 b. (36s15t−32s−95t12)12
- a. a34⋅a−14a−104 b. (27b23c−52b−73c12)13
- a. c53⋅c−13c−23 b. (8x53y−1227x−43y52)13
- a. m74⋅m−54m−24 b. (16m15n3281m95n−12)14
- Answer
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1. a. c78 b. p9 c. 1r
3. a. y54 b. x8 c. 1m
5. a. 81q2 b. a12b
7. a. 8u14 b. 8p12q34
9. a. r72 b. 6st
11. a. c2 b. 2x3y
Exercise SET G: writing exercises
- Show two different algebraic methods to simplify 432. Explain all your steps.
- Explain why the expression (−16)32 cannot be evaluated.
- Answer
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1. Answers will vary.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. What does this checklist tell you about your mastery of this section? What steps will you take to improve?