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Exponents And Powers

Question
CBSEENMA7001021
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Simplify:

(i) (− 4)3 

(ii) (− 3) × (− 2)3

(iii) (− 3)2 × (− 5)2 

(iv)(− 2)3 × (−10)3

Solution

(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

Some More Questions From Exponents and Powers Chapter

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

Express the following numbers using exponential notation:

(i) 512 (ii) 343

(iii) 729 (iv) 3125

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

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

(i) 648 (ii) 405

(iii) 540 (iv) 3,600

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

Simplify:

(i) (− 4)3 

(ii) (− 3) × (− 2)3

(iii) (− 3)2 × (− 5)2 

(iv)(− 2)3 × (−10)3

Compare the following numbers:

(i) 2.7 × 1012; 1.5 × 108

(ii) 4 × 1014; 3 × 1017

Say true or false and justify your answer:

(i) 10 × 1011 = 10011 (ii) 23 > 52

(iii) 23 × 32 = 65 (iv) 30 = (1000)0

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