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Express each of the following as a product of prime factors only in exponential form:
$(i)$. $108\times192$
$(ii)$. $270$
$(iii)$. $729\times64$
$(iv)$. $768$
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:
$(i)$. $108\times192$
$=(2\times 2\times 3\times 3\times 3)\times(2\times2\times2\times2\times2\times2\times3)$
$=(2^2\times3^3)\times(2^6\times3)$
$=2^{2+6}\times3^{3+1}$
$=2^8\times3^4$
$(ii)$. $270$
$=2\times3\times3\times3\times5$
$=2\times3^3\times5$
$(iii)$. $729\times64$
$=3\times3\times3\times3\times3\times3\times2\times2\times2\times2\times2\times2$
$=3^6\times2^6$
$(iv)$. $768$
$=2\times2\times2\times2\times2\times2\times2\times2\times3$
$=2^8\times3$
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