Chapter 6: Chapter 6

Problem 72

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Simplify (a) \(2^{3} \cdot 2^{2}\) (b) \(\mathrm{a}^{3} \cdot \mathrm{a}^{5}\) (c) \(x^{6} \cdot x^{4}\)

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(a) \(2^{5}\) (b) \(a^{8}\) (c) \(x^{10}\)

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TABLE OF CONTENTS

Step 1: a) Simplify \(2^{3} \cdot 2^{2}\)

We are multiplying two numbers with the same base (2), so we can apply the product rule of exponents to add the exponents: \(2^{3} \cdot 2^{2} = 2^{3+2}\). Now, simply add the exponents: \(3+2 = 5\). Therefore, the simplified expression is: \(2^{5}\).

Step 2: b) Simplify \(a^{3} \cdot a^{5}\)

We are multiplying two numbers with the same base (a), so we can apply the product rule of exponents to add the exponents: \(a^{3} \cdot a^{5} = a^{3+5}\). Now, simply add the exponents: \(3+5 = 8\). Therefore, the simplified expression is: \(a^{8}\).

Step 3: c) Simplify \(x^{6} \cdot x^{4}\)

We are multiplying two numbers with the same base (x), so we can apply the product rule of exponents to add the exponents: \(x^{6} \cdot x^{4} = x^{6+4}\). Now, simply add the exponents: \(6+4 = 10\). Therefore, the simplified expression is: \(x^{10}\).

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Chapter 6: Chapter 6

Simplify (a) \(2^{3} \cdot 2^{2}\) (b) \(\mathrm{a}^{3} \cdot \mathrm{a}^{5}\) (c) \(x^{6} \cdot x^{4}\)

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Step 1: a) Simplify \(2^{3} \cdot 2^{2}\)

Step 2: b) Simplify \(a^{3} \cdot a^{5}\)

Step 3: c) Simplify \(x^{6} \cdot x^{4}\)

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Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Chapter 21

Chapter 22

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 29

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 36

Chapter 37

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

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Chapter 46

Chapter 47

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