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Exponents and Powers
Question
Wired Faculty App

Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192 (ii) 270

(iii) 729 × 64 (iv) 768

Answer

(i) 108 × 192

= (2 × 2 × 3 × 3 × 3) × (2 × 2 × 2 × 2 × 2 × 2 × 3)

= (22 × 33) × (26 × 3)

= 26 + 2 × 33 + 1 (am × an = am+n)

= 28 × 34

(ii) 270 = 2 × 3 × 3 × 3 × 5 = 2 × 33 × 5

(iii) 729 × 64 = (3 × 3 × 3 × 3 × 3 × 3) × (2 × 2 × 2 × 2 × 2 × 2)

= 36 × 26

(iv) 768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 28 × 3

Sponsor Area

Some More Questions From Exponents and Powers Chapter

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

Express each of the following as a product of prime factors only in exponential form:

(i) 108 × 192 (ii) 270

(iii) 729 × 64 (iv) 768

Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Find the number from each of the following expanded forms:

(a) 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100

(b) 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100

(c) 3 × 104 + 7 × 102 + 5 × 100

(d) 9 × 105 + 2 × 102 + 3 × 101

Express the following numbers in standard form:

(i) 5, 00, 00, 000

(ii) 70, 00, 000

(iii) 3, 18, 65, 00, 000

(iv) 3, 90, 878

(v) 39087.8

(vi) 3908.78