Question

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

(i) 108 x 192 

(ii) 270 

(iii) 729 x 64 

(iv) 768

Answer 1

(i) 108 x 192

108 = 2 x 2 x 3 x 3 x 3

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

∴ 108 x 192 = (2 x 2 x 3 x 3 x 3) x (2 x 2 x 2 x 2 x 2 x 2 x 3)

= 2⁸ x 3⁴

Thus 108 x 192 = 2⁸ x 3⁴

(ii) 270

We have 270 = 2 x 3 x 3 x 3 x 5

= 2¹ x 3³ x 5¹

= 2 x 3³ x 5

So 270 = 2 x 3³ x 5

(iii) 729 x 64

729 = 3 x 3 x 3 x 3 x 3 x 3

64 = 2 x 2 x 2 x 2 x 2 x 2

729 x 64 = (3 x 3 x 3 x 3 x 3 x 3) x (2 x 2 x 2 x 2 x 2 x 2)

= 3⁶ x 2⁶

∴ 729 x 64 = 3⁶ x 2⁶

(iv) 768

We have 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

= 2⁸ x 3¹

= 2⁸ x 3

Thus 768 = 2⁸ x 3