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in Algebra by (26.1k points)
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Express the following as a product of factors only in exponential form 

(i) 108 x 192 

(ii) 270 

(iii) 729 x 64 

(iv) 768

1 Answer

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Best answer

(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

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