Q.4.    Express each of the following as a product of prime factors only in exponential form:            $(i)\: 108\times 192$          $(ii)\: 270$        $(iii)\: 729\times 64$       $(iv)\: 768$

$(i)\: 108\times 192$

 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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