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6.5E: Exercises

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Practice Makes Perfect

Simplify Expressions Using the Quotient Property for Exponents

In the following exercises, simplify.

Exercise 6.5E.1
  1. x18x3
  2. 51253
Exercise 6.5E.2
  1. y20y10
  2. 71672
Answer
  1. y10
  2. 714
Exercise 6.5E.3
  1. p21p7
  2. 41644
Exercise 6.5E.4
  1. u24u3
  2. 91595
Answer
  1. u21
  2. 910
Exercise 6.5E.5
  1. q18q36
  2. 102103
Exercise 6.5E.6
  1. t10t40
  2. 8385
Answer
  1. 1t30
  2. 164
Exercise 6.5E.7
  1. bb9
  2. 446
Exercise 6.5E.8
  1. xx7
  2. 10103
Answer
  1. 1x6
  2. 1100

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

Exercise 6.5E.9
  1. 200
  2. b0
Exercise 6.5E.10
  1. 130
  2. k0
Answer
  1. 1
  2. 1
Exercise 6.5E.11
  1. 270
  2. (270)
Exercise 6.5E.12
  1. 150
  2. (150)
Answer
  1. −1
  2. −1
Exercise 6.5E.13
  1. (25x)0
  2. 25x0
Exercise 6.5E.14
  1. (6y)0
  2. 6y0
Answer
  1. 1
  2. 6
Exercise 6.5E.15
  1. (12x)0
  2. (56p4q3)0
Exercise 6.5E.16
  1. 7y0(17y)0
  2. (93c7d15)0
Answer
  1. 7
  2. 1
Exercise 6.5E.17
  1. 12n018m0
  2. (12n)0(18m)0
Exercise 6.5E.18
  1. 15r022s0
  2. (15r)0(22s)0
Answer
  1. −7
  2. 0

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

Exercise 6.5E.19
  1. (34)3
  2. (p2)5
  3. (xy)6
Exercise 6.5E.20
  1. (25)2
  2. (x3)4
  3. (ab)5
Answer
  1. 425
  2. x481
  3. (ab)5
Exercise 6.5E.21
  1. (a3b)4
  2. (54m)2
Exercise 6.5E.22
  1. (a3b)4
  2. (103q)4
Answer
  1. x38y3
  2. 10,00081q4

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

Exercise 6.5E.23

(a2)3a4

Exercise 6.5E.24

(p3)4p5

Answer

p7

Exercise 6.5E.25

(y3)4y10

Exercise 6.5E.26

(x4)5x15

Answer

x5

Exercise 6.5E.27

u6(u3)2

Exercise 6.5E.28

v20(v4)5

Answer

1

Exercise 6.5E.29

m12(m8)3

Exercise 6.5E.30

n8(n6)4

Answer

1n16

Exercise 6.5E.31

(p9p3)5

Exercise 6.5E.32

(q8q2)3

Answer

q18

Exercise 6.5E.33

(r2r6)3

Exercise 6.5E.34

(m4m7)4

Answer

1m12

Exercise 6.5E.35

(pr11)2

Exercise 6.5E.36

(ab6)3

Answer

a3b18

Exercise 6.5E.37

(w5x3)8

Exercise 6.5E.38

(y4z10)5

Answer

y20z50

Exercise 6.5E.39

(2j33k)4

Exercise 6.5E.40

(3m55n)3

Answer

27m15125n3

Exercise 6.5E.41

(3c24d6)3

Exercise 6.5E.42

(5u72v3)4

Answer

625u2816v12

Exercise 6.5E.43

(k2k8k3)2

Exercise 6.5E.44

(j2j5j4)3

Answer

j9

Exercise 6.5E.45

(t2)5(t4)2(t3)7

Exercise 6.5E.46

(q3)6(q2)3(q4)8

Answer

1q8

Exercise 6.5E.47

(2p2)4(3p4)2(6p3)2

Exercise 6.5E.48

(2k3)2(6k2)4(9k4)2

Answer

64k6

Exercise 6.5E.49

(4m3)2(5m4)3(10m6)3

Exercise 6.5E.50

(10n2)3(4n5)2(2n8)2

Answer

−4,000

Divide Monomials

In the following exercises, divide the monomials.

Exercise 6.5E.51

56b8÷7b2

Exercise 6.5E.52

63ν10÷9v2

Answer

7v8

Exercise 6.5E.53

88y15÷8y3

Exercise 6.5E.54

72u12÷12u4

Answer

6u8

Exercise 6.5E.55

45a6b815a10b2

Exercise 6.5E.56

54x9y318x6y15

Answer

3x3y12

Exercise 6.5E.57

15r4s918r9s2

Exercise 6.5E.58

20m8n430m5n9

Answer

2m33n5

Exercise 6.5E.59

18a4b827a9b5

Exercise 6.5E.60

45x5y960x8y6

Answer

3y34x3

Exercise 6.5E.61

64q11r9s348q6r8s5

Exercise 6.5E.62

65a10b8c542a7b6c8

Answer

65a3b242c3

Exercise 6.5E.63

(10m5n4)(5m3n6)25m7n5

Exercise 6.5E.64

(18p4q7)(6p3q8)36p12q10

Answer

3q5p5

Exercise 6.5E.65

(6a4b3)(4ab5)(12a2b)(a3b)

Exercise 6.5E.66

(4u2v5)(15u3v)(12u3v)(u4v)

Answer

5v4u2

Mixed Practice

Exercise 6.5E.67
  1. 24a5+2a5
  2. 24a52a5
  3. 24a52a5
  4. 24a5÷2a5
Exercise 6.5E.68
  1. 15n10+3n10
  2. 15n103n10
  3. 15n103n10
  4. 15n10÷3n10
Answer
  1. 18n10
  2. 12n10
  3. 45n20
  4. 5
Exercise 6.5E.69
  1. p4p6
  2. (p4)6
Exercise 6.5E.70
  1. q5q3
  2. (q5)3
Answer
  1. q8
  2. q15
Exercise 6.5E.71
  1. y3y
  2. yy3
Exercise 6.5E.72
  1. z6z5
  2. z5z6
Answer
  1. z
  2. 1z
Exercise 6.5E.73

(8x5)(9x)÷6x3

Exercise 6.5E.74

(4y)(12y7)÷8y2

Answer

6y6

Exercise 6.5E.75

27a73a3+54a99a5

Exercise 6.5E.76

32c114c5+42c96c3

Answer

15c6

Exercise 6.5E.77

32y58y260y105y7

Exercise 6.5E.78

48x66x435x97x7

Answer

3x2

Exercise 6.5E.79

63r6s39r4s272r2s26s

Exercise 6.5E.80

56y4z57y3z345y2z25y

Answer

yz2

Everyday Math

Exercise 6.5E.81

Memory One megabyte is approximately 106 bytes. One gigabyte is approximately 109 bytes. How many megabytes are in one gigabyte?

Exercise 6.5E.82

Memory One gigabyte is approximately 109 bytes. One terabyte is approximately 1012 bytes. How many gigabytes are in one terabyte?

Answer

103

Writing Exercises

Exercise 6.5E.83

Jennifer thinks the quotient a24a6 simplifies to a4. What is wrong with her reasoning?

Exercise 6.5E.84

Maurice simplifies the quotient d7d by writing d7d=7. What is wrong with his reasoning?

Answer

Answers will vary.

Exercise 6.5E.85

When Drake simplified 30 and (3)0 he got the same answer. Explain how using the Order of Operations correctly gives
different answers.

Exercise 6.5E.86

Robert thinks x0 simplifies to 0. What would you say to convince Robert he is wrong?

Answer

Answers will vary.

Self Check

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

This is a table that has six rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “simplify expressions using the Quotient Property for Exponents,” “simplify expressions with zero exponents,” “simplify expressions using the Quotient to a Power Property,” “simplify expressions by applying several properties,” and “divide monomials.” The rest of the cells are blank.

b. On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?


This page titled 6.5E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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