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Learn Exercise 13.1 with Free Lessons & Tips

Find the value of:

(i) 26 (ii) 93

(iii) 112 (iv)54

(i) 26 = 2 × 2 × 2 × 2 × 2 × 2 = 64

(ii) 93 = 9 × 9 × 9 = 729

(iii) 112 = 11 × 11 = 121

(iv)54 = 5 × 5 × 5 × 5 = 625

Comments

Express the following in exponential form:

(i) 6 × 6 × 6 × 6 (ii) t × t

(iii) b × b × b × b (iv) 5 × 5 × 7 ×7 × 7

(v) 2 × 2 × a × a (vi) a × a × a × c × c × c × c × d

(i) 6 × 6 × 6 × 6 = 64

(ii) t × t= t2

(iii) b × b × b × b = b4

(iv) 5 × 5 × 7 × 7 × 7 = 52 × 73

(v) 2 × 2 × a × a = 22 × a2

(vi) a × a × a × c × c × c × c × d = a3c4d

Comments

Express the following numbers using exponential notation:

(i) 512 (ii) 343

(iii) 729 (iv) 3125

(i) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 29

(ii) 343 = 7 × 7 × 7 = 73

(iii) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 36

(iv) 3125 = 5 × 5 × 5 × 5 × 5 = 55

Comments

Identify the greater number, wherever possible, in each of the following?

(i) 43 or 34 (ii) 53 or 35

(iii) 28 or 82 (iv) 1002 or 2100

(v) 210 or 102

(i) 43 = 4 × 4 × 4 = 64

34 = 3 × 3 × 3 × 3 = 81

Therefore, 34 > 43

(ii) 53 = 5 × 5 × 5 =125

35 = 3 × 3 × 3 × 3 × 3 = 243

Therefore, 35 > 53

(iii) 28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

82 = 8 × 8 = 64

Therefore, 28 > 82

(iv)1002 or 2100

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

2100 = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 ×1024 × 1024

1002 = 100 × 100 = 10000

Therefore, 2100 > 1002

(v) 210 and 102

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

102 = 10 × 10 = 100

Therefore, 210 > 102

Comments

Express each of the following as product of powers of their prime factors:

(i) 648 (ii) 405

(iii) 540 (iv) 3,600

(i) 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 23. 34

(ii) 405 = 3 × 3 × 3 × 3 × 5 = 34 . 5

(iii) 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22. 33. 5

(iv) 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 24. 32. 52

Comments

Simplify:

(i) 2 × 103 (ii) 72 × 22

(iii) 23 × 5 (iv) 3× 44

(v) 0 × 102 ­­­­­ (vi) 52 × 33

(vii) 24 × 32 (viii) 32 × 104

(i) 2 × 103 = 2 × 10 × 10 × 10 = 2 × 1000 = 2000

(ii) 72 × 22 = 7 × 7 × 2 × 2 = 49 × 4 = 196

(iii) 23 × 5 = 2 × 2 × 2 × 5 = 8 × 5 = 40

(iv) 3 × 44 = 3 × 4 × 4 × 4 × 4 = 3 × 256 = 768

(v) 0 × 102 = 0 × 10 × 10 = 0

(vi) 52 × 33 = 5 × 5 × 3 × 3 × 3 = 25 × 27 = 675

(vii) 24 × 32 = 2 × 2 × 2 × 2 × 3 × 3 = 16 × 9 = 144

(viii) 32 × 104 = 3 × 3 × 10 × 10 × 10 × 10 = 9 × 10000 = 90000

Comments

Simplify:

(i) (− 4)3 (ii) (− 3) × (− 2)3

(iii) (− 3)2 × (− 5)2 (iv)(− 2)3 × (−10)3

(i) (−4)3 = (−4) × (−4) × (−4) = −64

(ii) (−3) × (−2)3 = (−3) × (−2) × (−2) × (−2) = 24

(iii) (−3)2 × (−5)2 = (−3) × (−3) × (−5) × (−5) = 9 × 25 = 225

(iv) (−2)3 × (−10)3 = (−2) × (−2) × (−2) × (−10) × (−10) × (−10)

= (−8) × (−1000) = 8000

Comments

Compare the following numbers: (i) 2.7 × 1012; 1.5 × 108 (ii) 4 × 1014; 3 × 1017

(i) 2.7 × 1012; 1.5 × 108

2.7 × 1012 > 1.5 × 108

(ii) 4 × 1014; 3 × 1017

3 × 1017 > 4 × 1014

Comments

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