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
it is the required prime factor product form (ii) 270 2 192 2 96 2 48 2 24 2 12 2 6 3 3 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) \[\mathbf{729\times 64}\] \[729\times 64=3\times 3\times 3\times 3\times 3\times 3\times 2\times 2\times 2\times 2\times 2\times 2\] 2 270 3 135 3 45 3 15 5 5 1
3 729 3 243 3 81 3 27 3 9 3 3 1
\[={{3}^{6}}\times {{2}^{6}}\] It is the required prime factor product form. (iv) 768 2 64 2 32 2 16 2 8 2 4 2 2 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. 2 768 2 384 2 192 2 96 2 48 2 24 2 12 2 6 3 3 1
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