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  • Express each of the following as a product of prime factors only in exponential form: 108 times 192

Q.4.    Express each of the following as a product of prime factors only in exponential form:

            (i)\: 108\times 192          (ii)\: 270        (iii)\: 729\times 64       (iv)\: 768

Answers (1)

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(i)\: 108\times 192

2 108
2 54
3 27
3 9
3 3
  1

 

2 192
2 96
2 48
2 24
2 12
2 6
3 3
  1

 

108\times 192=(2^2\times 3^3)\times (2^6\times 3)

                   =2^{(2+6)}\times 3^{(3+1)}

                =2^8\times 3^4

 

 

(ii)\: 270

2 270
3 135
3 45
3 15
5 5
  1

270=2\times 3^3\times 5

 

(iii)\: 729\times 64

3 729
3 243
3 81
3 27
3 9
3 3
  1

 

2 64
2 32
2 16
2 8
2 4
2 2
  1

729\times 64=3^6\times 2^6

 

(iv)\: 768

2 768
2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
  1

 

768=2^8\times 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

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