• # question_answer 5) Express each of the following as product of powers of their prime factors: (i) 648                                    (ii) 405                                   (iii) 540                                  (iv) 3600.

(i) 648

 2 648 2 324 2 162 2 81 2 27 2 9 2 3 2 1
$\therefore$  $648=2\times 2\times 2\times 3\times 3\times 3\times 3$                 It is the required prime factor product form.                 (ii) 405  3 405 3 135 3 45 3 15 5 5 1
$\therefore$  $405=3\times 3\times 3\times 3\times 5$                 $={{3}^{4}}\times 5$                 It is the required prime factor product form.                 (iii) 540  2 540 2 270 3 135 3 45 3 15 5 5 1
$\therefore$  $540=2\times 2\times 3\times 3\times 3\times 5$                 $={{2}^{2}}\times {{3}^{3}}\times 5$                 It is the required prime factor product form.                 (iv) 3600  2 3600 2 1800 2 900 2 450 3 225 3 75 5 25 5 5 1
$\therefore$  $3600=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5$                 $={{2}^{4}}\times {{3}^{2}}\times {{5}^{2}}$                 It is the required prime factor product form.

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