7th Class Mathematics Exponents and Power

  • question_answer 12) Express each of the following as a product of prime factors only in exponential form: (i) \[108\times 192\]                       (ii) \[\text{27}0\]                                              (iii) \[729\times 64\]                       (iv) \[768\]

    Answer:

                    (i) \[\mathbf{108\times 192}\]                 \[108\times 192\]\[=(2\times 2\times 3\times 3\times 3)\times (2\times 2\times 2\times 2\times 2\times 2\times 3)\] \[=2\times 2\times 3\times 3\times 3\times 2\times 2\times 2\times 2\times 2\times 2\times 3\] \[=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3\] \[={{2}^{8}}\times {{3}^{4}}\]

    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
                    it is the required prime factor product form                 (ii) 270                
    2 270
    3 135
    3 45
    3 15
    5 5
    1
    \[\therefore \]  \[270=2\times 3\times 3\times 3\times 5={{2}^{1}}\times {{3}^{3}}\times {{5}^{1}}\]                 It is the required prime factor product form.                 (iii) \[\mathbf{729\times 64}\]                 \[729\times 64=3\times 3\times 3\times 3\times 3\times 3\times 2\times 2\times 2\times 2\times 2\times 2\]                
    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
                    \[={{3}^{6}}\times {{2}^{6}}\]                 It is the required prime factor product form.                 (iv) 768                
    2 768
    2 384
    2 192
    2 96
    2 48
    2 24
    2 12
    2 6
    3 3
    1
    \[\therefore \]  \[768=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\] \[={{2}^{8}}\times {{3}^{1}}\]     It is the required prime factor product form.

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