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10.2 Use Multiplication Properties of Exponents

Product, Power, and Product-to-a-Power rules for adding and multiplying exponents, stacked several at a time and applied to multiplying monomials.

Prealgebra 2e, 10.2 Use Multiplication Properties of Exponents

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90 exercises

10.2 Exercise 1

Before you get started, take this readiness quiz.

Simplify: 34·34.\frac{3}{4} \cdot \frac{3}{4} .
If you missed the problem, review the reference.

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10.2 Exercise 2

Simplify: (−2)(−2)(−2).\left(−2\right) \left(−2\right) \left(−2\right) .
If you missed the problem, review the reference.

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10.2 Exercise 3

Simplify:

  1. ⓐ 535^{3}
  2. ⓑ 919^{1}

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10.2 Exercise 4

Simplify:

  1. ⓐ 434^{3}
  2. ⓑ 11111^{1}

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10.2 Exercise 5

Simplify:

  1. ⓐ 343^{4}
  2. ⓑ 21121^{1}

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10.2 Exercise 6

Simplify:

  1. ⓐ (78)2\left(\frac{7}{8}\right)^{2}
  2. ⓑ (0.74)2\left(0.74\right)^{2}

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10.2 Exercise 7

Simplify:

  1. ⓐ (58)2\left(\frac{5}{8}\right)^{2}
  2. ⓑ (0.67)2\left(0.67\right)^{2}

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10.2 Exercise 8

Simplify:

  1. ⓐ (25)3\left(\frac{2}{5}\right)^{3}
  2. ⓑ (0.127)2\left(0.127\right)^{2}

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10.2 Exercise 9

Simplify:

  1. ⓐ (−3)4\left(−3\right)^{4}
  2. ⓑ −34−3^{4}

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10.2 Exercise 10

Simplify:

  1. ⓐ (−2)4\left(−2\right)^{4}
  2. ⓑ −24−2^{4}

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10.2 Exercise 11

Simplify:

  1. ⓐ (−8)2\left(−8\right)^{2}
  2. ⓑ −82−8^{2}

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10.2 Exercise 13

Simplify: x7·x8.x^{7} \cdot x^{8} .

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10.2 Exercise 14

Simplify: x5·x11.x^{5} \cdot x^{11} .

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10.2 Exercise 16

Simplify: p9·p.p^{9} \cdot p .

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10.2 Exercise 17

Simplify: m·m7.m \cdot m^{7} .

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10.2 Exercise 19

Simplify: 6·69.6 \cdot 6^{9} .

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10.2 Exercise 20

Simplify: 96·99.9^{6} \cdot 9^{9} .

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10.2 Exercise 22

Simplify: y24·y19.y^{24} \cdot y^{19} .

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10.2 Exercise 23

Simplify: z15·z24.z^{15} \cdot z^{24} .

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10.2 Exercise 25

Simplify: x7·x5·x9.x^{7} \cdot x^{5} \cdot x^{9} .

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10.2 Exercise 26

Simplify: y3·y8·y4.y^{3} \cdot y^{8} \cdot y^{4} .

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10.2 Exercise 28

Simplify:

  1. ⓐ (x7)4\left(x^{7}\right)^{4}
  2. ⓑ (74)8\left(7^{4}\right)^{8}

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10.2 Exercise 29

Simplify:

  1. ⓐ (x6)9\left(x^{6}\right)^{9}
  2. ⓑ (86)7\left(8^{6}\right)^{7}

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10.2 Exercise 31

Simplify: (−14x)2.\left(−14 x\right)^{2} .

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10.2 Exercise 32

Simplify: (−12a)2.\left(−12 a\right)^{2} .

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10.2 Exercise 34

Simplify: (−4xy)4.\left(−4 x y\right)^{4} .

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10.2 Exercise 35

Simplify: (6xy)3.\left(6 x y\right)^{3} .

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10.2 Exercise 36

Simplify: (x2)6(x5)4.\left(x^{2}\right)^{6} \left(x^{5}\right)^{4} .

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10.2 Exercise 37

Simplify: (x4)3(x7)4.\left(x^{4}\right)^{3} \left(x^{7}\right)^{4} .

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10.2 Exercise 38

Simplify: (y9)2(y8)3.\left(y^{9}\right)^{2} \left(y^{8}\right)^{3} .

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10.2 Exercise 39

Simplify: (−7x3y4)2.\left(- 7 x^{3} y^{4}\right)^{2} .

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10.2 Exercise 40

Simplify: (−8x4y7)3.\left(- 8 x^{4} y^{7}\right)^{3} .

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10.2 Exercise 41

Simplify: (−3a5b6)4.\left(- 3 a^{5} b^{6}\right)^{4} .

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10.2 Exercise 42

Simplify: (6n)2(4n3).\left(6 n\right)^{2} \left(4 n^{3}\right) .

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10.2 Exercise 43

Simplify: (7n)2(2n12).\left(7 n\right)^{2} \left(2 n^{12}\right) .

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10.2 Exercise 44

Simplify: (4m)2(3m3).\left(4 m\right)^{2} \left(3 m^{3}\right) .

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10.2 Exercise 45

Simplify: (3p2q)4(2pq2)3.\left(3 p^{2} q\right)^{4} \left(2 p q^{2}\right)^{3} .

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10.2 Exercise 46

Simplify: (u3v2)5(4uv4)3.\left(u^{3} v^{2}\right)^{5} \left(4 u v^{4}\right)^{3} .

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10.2 Exercise 47

Simplify: (5x2y3)2(3xy4)3.\left(5 x^{2} y^{3}\right)^{2} \left(3 x y^{4}\right)^{3} .

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10.2 Exercise 48

Multiply: (4x2)(−5x3).\left(4 x^{2}\right) \left(- 5 x^{3}\right) .

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10.2 Exercise 49

Multiply: (7x7)(−8x4).\left(7 x^{7}\right) \left(- 8 x^{4}\right) .

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10.2 Exercise 50

Multiply: (−9y4)(−6y5).\left(- 9 y^{4}\right) \left(- 6 y^{5}\right) .

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10.2 Exercise 51

Multiply: (34c3d)(12cd2).\left(\frac{3}{4} c^{3} d\right) \left(12 c d^{2}\right) .

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10.2 Exercise 52

Multiply: (45m4n3)(15mn3).\left(\frac{4}{5} m^{4} n^{3}\right) \left(15 m n^{3}\right) .

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10.2 Exercise 53

Multiply: (23p5q)(18p6q7).\left(\frac{2}{3} p^{5} q\right) \left(18 p^{6} q^{7}\right) .

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10.2 Exercise 54

Simplify each expression with exponents.

454^{5}

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10.2 Exercise 56

Simplify each expression with exponents.

(12)2\left(\frac{1}{2}\right)^{2}

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10.2 Exercise 58

Simplify each expression with exponents.

(0.2)3\left(0.2\right)^{3}

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10.2 Exercise 60

Simplify each expression with exponents.

(−5)4\left(−5\right)^{4}

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10.2 Exercise 62

Simplify each expression with exponents.

−54−5^{4}

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10.2 Exercise 64

Simplify each expression with exponents.

−104−10^{4}

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10.2 Exercise 66

Simplify each expression with exponents.

(−23)3\left(- \frac{2}{3}\right)^{3}

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10.2 Exercise 68

Simplify each expression with exponents.

−0.52- 0.5^{2}

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10.2 Exercise 70

Simplify each expression using the Product Property of Exponents.

x3·x6x^{3} \cdot x^{6}

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10.2 Exercise 72

Simplify each expression using the Product Property of Exponents.

a·a4a \cdot a^{4}

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10.2 Exercise 74

Simplify each expression using the Product Property of Exponents.

35·393^{5} \cdot 3^{9}

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10.2 Exercise 76

Simplify each expression using the Product Property of Exponents.

z·z2·z3z \cdot z^{2} \cdot z^{3}

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10.2 Exercise 78

Simplify each expression using the Product Property of Exponents.

xa·x2x^{a} \cdot x^{2}

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10.2 Exercise 80

Simplify each expression using the Product Property of Exponents.

ya·yby^{a} \cdot y^{b}

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10.2 Exercise 82

Simplify each expression using the Power Property of Exponents.

(u4)2\left(u^{4}\right)^{2}

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10.2 Exercise 84

Simplify each expression using the Power Property of Exponents.

(y5)4\left(y^{5}\right)^{4}

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10.2 Exercise 86

Simplify each expression using the Power Property of Exponents.

(102)6\left(10^{2}\right)^{6}

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10.2 Exercise 88

Simplify each expression using the Power Property of Exponents.

(x15)6\left(x^{15}\right)^{6}

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10.2 Exercise 90

Simplify each expression using the Power Property of Exponents.

(x2)y\left(x^{2}\right)^{y}

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10.2 Exercise 92

Simplify each expression using the Power Property of Exponents.

(5x)y\left(5^{x}\right)^{y}

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10.2 Exercise 94

Simplify each expression using the Product to a Power Property.

(5a)2\left(5 a\right)^{2}

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10.2 Exercise 96

Simplify each expression using the Product to a Power Property.

(−6m)3\left(- 6 m\right)^{3}

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10.2 Exercise 98

Simplify each expression using the Product to a Power Property.

(4rs)2\left(4 r s\right)^{2}

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10.2 Exercise 100

Simplify each expression using the Product to a Power Property.

(4xyz)4\left(4 x y z\right)^{4}

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10.2 Exercise 102

Simplify each expression.

(x2)4·(x3)2\left(x^{2}\right)^{4} \cdot \left(x^{3}\right)^{2}

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10.2 Exercise 104

Simplify each expression.

(a2)6·(a3)8\left(a^{2}\right)^{6} \cdot \left(a^{3}\right)^{8}

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10.2 Exercise 106

Simplify each expression.

(3x)2(5x)\left(3 x\right)^{2} \left(5 x\right)

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10.2 Exercise 108

Simplify each expression.

(5a)2(2a)3\left(5 a\right)^{2} \left(2 a\right)^{3}

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10.2 Exercise 110

Simplify each expression.

(2m6)3\left(2 m^{6}\right)^{3}

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10.2 Exercise 112

Simplify each expression.

(10x2y)3\left(10 x^{2} y\right)^{3}

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10.2 Exercise 114

Simplify each expression.

(−2a3b2)4\left(−2 a^{3} b^{2}\right)^{4}

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10.2 Exercise 116

Simplify each expression.

(23x2y)3\left(\frac{2}{3} x^{2} y\right)^{3}

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10.2 Exercise 118

Simplify each expression.

(8a3)2(2a)4\left(8 a^{3}\right)^{2} \left(2 a\right)^{4}

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10.2 Exercise 120

Simplify each expression.

(10p4)3(5p6)2\left(10 p^{4}\right)^{3} \left(5 p^{6}\right)^{2}

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10.2 Exercise 122

Simplify each expression.

(12x2y3)4(4x5y3)2\left(\frac{1}{2} x^{2} y^{3}\right)^{4} \left(4 x^{5} y^{3}\right)^{2}

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10.2 Exercise 124

Simplify each expression.

(3m2n)2(2mn5)4\left(3 m^{2} n\right)^{2} \left(2 m n^{5}\right)^{4}

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10.2 Exercise 126

Multiply the following monomials.

(12x2)(−5x4)\left(12 x^{2}\right) \left(−5 x^{4}\right)

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10.2 Exercise 128

Multiply the following monomials.

(−8u6)(−9u)\left(−8 u^{6}\right) \left(−9 u\right)

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10.2 Exercise 130

Multiply the following monomials.

(15r8)(20r3)\left(\frac{1}{5} r^{8}\right) \left(20 r^{3}\right)

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10.2 Exercise 132

Multiply the following monomials.

(4a3b)(9a2b6)\left(4 a^{3} b\right) \left(9 a^{2} b^{6}\right)

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10.2 Exercise 134

Multiply the following monomials.

(47xy2)(14xy3)\left(\frac{4}{7} x y^{2}\right) \left(14 x y^{3}\right)

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10.2 Exercise 136

Multiply the following monomials.

(23x2y)(34xy2)\left(\frac{2}{3} x^{2} y\right) \left(\frac{3}{4} x y^{2}\right)

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10.2 Exercise 138

Email Janet emails a joke to six of her friends and tells them to forward it to six of their friends, who forward it to six of their friends, and so on. The number of people who receive the email on the second round is 62,6^{2} , on the third round is 63,6^{3} , as shown in the table. How many people will receive the email on the eighth round? Simplify the expression to show the number of people who receive the ema…

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10.2 Exercise 140

Use the Product Property for Exponents to explain why x·x=x2.x \cdot x = x^{2} .

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10.2 Exercise 142

Jorge thinks (12)2\left(\frac{1}{2}\right)^{2} is 1.1 . What is wrong with his reasoning?

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Adapted from Prealgebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Prealgebra 2e. Imported at revision 77a933c.