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17.4E: Exercises

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Practice Makes Perfect

Exercise SET A: simplify expressions with a1n

In the following exercises, write as a radical expression.

  1. a. x12 b. y13 c. z14
  2. a. r12 b. s13 c. t14
  3. a. u15 b. v19 c. w120
  4. a. g17 b. h15 c. j125
Answer

1. a. x b. 3y c. 4z

3. a. 5u b. 9v c. 20w

Exercise Set B: simplify expressions with a1n

In the following exercises, write with a rational exponent.

  1. a. 7x b. 9y c. 5f
  2. a. 84 b. 10s c. 4t
  3. a. 37c b. 712d c. 246b
  4. a. 45x b. 89y c. 753z
  5. a. 21p b. 48q c. 4636r
  6. a. 325a b. 3b c. 840c
Answer

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.

  1. a. 8112 b. 12513 c. 6412
  2. a. 62514 b. 24315 c. 3215
  3. a. 1614 b. 1612 c. 62514
  4. a. 6413 b. 3215 c. 8114
  5. a. (216)13 b. 21613 c. (216)13
  6. a. (1000)13 b. 100013 c. (1000)13
  7. a. (81)14 b. 8114 c. (81)14
  8. a. (49)12 b. 4912 c. (49)12
  9. a. (36)12 b. 3612 c. (36)12
  10. a. (16)14 b. 1614 c. 1614
  11. a. (100)12 b. 10012 c. (100)12
  12. a. (32)15 b. (243)15 c. 12513
Answer

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.

  1. a. m5 b. (33y)7 c. 5(4x5y)3
  2. a. 4r7 b. (52pq)3 c. 4(12m7n)3
  3. a. 5u2 b. (36x)5 c. 4(18a5b)7
  4. a. 3a b. (421v)3 c. 4(2xy5z)2
Answer

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.

  1. a. 6452 b. 8132 c. (27)23
  2. a. 2532 b. 932 c. (64)23
  3. a. 3225 b. 2723 c. (25)12
  4. a. 10032 b. 4952 c. (100)32
  5. a. 932 b. 932 c. (9)32
  6. a. 6432 b. 6432 c. (64)32
Answer

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.

  1. a. c14c58 b. (p12)34 c. r45r95
  2. a. 652612 b. (b15)35 c. w27w97
  3. a. y12y34 b. (x12)23 c. m58m138
  4. a. q23q56 b. (h6)43 c. n35n85
  5. a. (27q32)43 b. (a13b23)32
  6. a. (64s37)16 b. (m43n12)34
  7. a. (16u13)34 b. (4p13q12)32
  8. a. (625n83)34 b. (9x25y35)52
  9. a. r52r12r32 b. (36s15t32s95t12)12
  10. a. a34a14a104 b. (27b23c52b73c12)13
  11. a. c53c13c23 b. (8x53y1227x43y52)13
  12. a. m74m54m24 b. (16m15n3281m95n12)14
Answer

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
  1. Show two different algebraic methods to simplify 432. Explain all your steps.
  2. Explain why the expression (16)32 cannot be evaluated.
Answer

1. Answers will vary.

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has 4 rows and 4 columns. The first row is a header row and it labels each column. The first column header is “I can…”, the second is “Confidently”, the third is “With some help”, and the fourth is “No, I don’t get it”. Under the first column are the phrases “simplify expressions with a to the power of 1 divided by n.”, “simplify expression with a to the power of m divided by n”, and “use the laws of exponents to simplify expression with rational exponents”. The other columns are left blank so that the learner may indicate their mastery level for each topic.
Figure 8.3.4

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


This page titled 17.4E: Exercises is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax.

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