# Express each of the following as a product of prime factors only in exponential form:$(i)$. $108\times192$$(ii). 270$$(iii)$. $729\times64$$(iv)$. $768$

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Given:

$(i)$. $108\times192$

$(ii)$. $270$

$(iii)$. $729\times64$

$(iv)$. $768$

To do: To express each of the above as the product of prime factors only in exponential form.

Solution:

$(i)$. $108\times192$

$=(2\times 2\times 3\times 3\times 3)\times(2\times2\times2\times2\times2\times2\times3)$

$=(2^2\times3^3)\times(2^6\times3)$

$=2^{2+6}\times3^{3+1}$

$=2^8\times3^4$

$(ii)$. $270$

$=2\times3\times3\times3\times5$

$=2\times3^3\times5$

$(iii)$. $729\times64$

$=3\times3\times3\times3\times3\times3\times2\times2\times2\times2\times2\times2$

$=3^6\times2^6$

$(iv)$. $768$

$=2\times2\times2\times2\times2\times2\times2\times2\times3$

$=2^8\times3$

Updated on 10-Oct-2022 13:38:51