6.5E: Exercises
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Practice Makes Perfect
Simplify Expressions Using the Quotient Property for Exponents
In the following exercises, simplify.
- x18x3
- 51253
- y20y10
- 71672
- Answer
-
- y10
- 714
- p21p7
- 41644
- u24u3
- 91595
- Answer
-
- u21
- 910
- q18q36
- 102103
- t10t40
- 8385
- Answer
-
- 1t30
- 164
- bb9
- 446
- xx7
- 10103
- Answer
-
- 1x6
- 1100
Simplify Expressions with Zero Exponents
In the following exercises, simplify.
- 200
- b0
- 130
- k0
- Answer
-
- 1
- 1
- −270
- −(270)
- −150
- −(150)
- Answer
-
- −1
- −1
- (25x)0
- 25x0
- (6y)0
- 6y0
- Answer
-
- 1
- 6
- (12x)0
- (−56p4q3)0
- 7y0(17y)0
- (−93c7d15)0
- Answer
-
- 7
- 1
- 12n0−18m0
- (12n)0−(18m)0
- 15r0−22s0
- (15r)0−(22s)0
- Answer
-
- −7
- 0
Simplify Expressions Using the Quotient to a Power Property
In the following exercises, simplify.
- (34)3
- (p2)5
- (xy)6
- (25)2
- (x3)4
- (ab)5
- Answer
-
- 425
- x481
- (ab)5
- (a3b)4
- (54m)2
- (a3b)4
- (103q)4
- Answer
-
- x38y3
- 10,00081q4
Simplify Expressions by Applying Several Properties
In the following exercises, simplify.
(a2)3a4
(p3)4p5
- Answer
-
p7
(y3)4y10
(x4)5x15
- Answer
-
x5
u6(u3)2
v20(v4)5
- Answer
-
1
m12(m8)3
n8(n6)4
- Answer
-
1n16
(p9p3)5
(q8q2)3
- Answer
-
q18
(r2r6)3
(m4m7)4
- Answer
-
1m12
(pr11)2
(ab6)3
- Answer
-
a3b18
(w5x3)8
(y4z10)5
- Answer
-
y20z50
(2j33k)4
(3m55n)3
- Answer
-
27m15125n3
(3c24d6)3
(5u72v3)4
- Answer
-
625u2816v12
(k2k8k3)2
(j2j5j4)3
- Answer
-
j9
(t2)5(t4)2(t3)7
(q3)6(q2)3(q4)8
- Answer
-
1q8
(−2p2)4(3p4)2(−6p3)2
(−2k3)2(6k2)4(9k4)2
- Answer
-
64k6
(−4m3)2(5m4)3(−10m6)3
(−10n2)3(4n5)2(2n8)2
- Answer
-
−4,000
Divide Monomials
In the following exercises, divide the monomials.
56b8÷7b2
63ν10÷9v2
- Answer
-
7v8
−88y15÷8y3
−72u12÷12u4
- Answer
-
−6u8
45a6b8−15a10b2
54x9y3−18x6y15
- Answer
-
−3x3y12
15r4s918r9s2
20m8n430m5n9
- Answer
-
2m33n5
18a4b8−27a9b5
45x5y9−60x8y6
- Answer
-
−3y34x3
64q11r9s348q6r8s5
65a10b8c542a7b6c8
- Answer
-
65a3b242c3
(10m5n4)(5m3n6)25m7n5
(−18p4q7)(−6p3q8)−36p12q10
- Answer
-
−3q5p5
(6a4b3)(4ab5)(12a2b)(a3b)
(4u2v5)(15u3v)(12u3v)(u4v)
- Answer
-
5v4u2
Mixed Practice
- 24a5+2a5
- 24a5−2a5
- 24a5⋅2a5
- 24a5÷2a5
- 15n10+3n10
- 15n10−3n10
- 15n10⋅3n10
- 15n10÷3n10
- Answer
-
- 18n10
- 12n10
- 45n20
- 5
- p4⋅p6
- (p4)6
- q5⋅q3
- (q5)3
- Answer
-
- q8
- q15
- y3y
- yy3
- z6z5
- z5z6
- Answer
-
- z
- 1z
(8x5)(9x)÷6x3
(4y)(12y7)÷8y2
- Answer
-
6y6
27a73a3+54a99a5
32c114c5+42c96c3
- Answer
-
15c6
32y58y2−60y105y7
48x66x4−35x97x7
- Answer
-
3x2
63r6s39r4s2−72r2s26s
56y4z57y3z3−45y2z25y
- Answer
-
−yz2
Everyday Math
Memory One megabyte is approximately 106 bytes. One gigabyte is approximately 109 bytes. How many megabytes are in one gigabyte?
Memory One gigabyte is approximately 109 bytes. One terabyte is approximately 1012 bytes. How many gigabytes are in one terabyte?
- Answer
-
103
Writing Exercises
Jennifer thinks the quotient a24a6 simplifies to a4. What is wrong with her reasoning?
Maurice simplifies the quotient d7d by writing ⧸d7⧸d=7. What is wrong with his reasoning?
- Answer
-
Answers will vary.
When Drake simplified −30 and (−3)0 he got the same answer. Explain how using the Order of Operations correctly gives
different answers.
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.
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?