Question

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

(i) 108 x 192

(ii) 270

(iii) 729 × 64

(iv) 768

Answer 1

(i) 108 x 192

= 2 × 2 × 3 × 3 × 3 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

= 2⁸ × 3⁴

It is the product of prime factor

(ii) 270

270 = 2 × 3 × 3 × 3 × 5

= 2 × 3³ × 5

It is required prime factor.

(iii) 729 × 64

729 = 3 × 3 × 3 × 3 × 3 × 3

64 = 2 × 2 × 2 × 2 × 2 × 2

∴ 729 × 64 = 3⁶ × 2⁶

It is the required prime factor.

(iv) 768

768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

= 2⁸ × 3¹ or = 2⁸ × 3

It is required prime factor.