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Express the following as a product of prime factors.$108\times192$
Given :
The given expression is $108\times192$.
To do:
We have to express the given expression as a product of prime factors.
Solution :
Prime factorisation of 108 and 192 is,
$108 = 2 \times 2 \times 3 \times 3 \times 3$
$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
Therefore,
$108\times192$ as a product of prime factors $= ( 2 \times 2 \times 3 \times 3 \times 3) \times (2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3)$
$= (2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2) \times (3 \times 3 \times 3 \times 3)$
$= 2^8 \times 3^4$.
Therefore, $108\times192$ as a product of prime factors is $2^8 \times 3^4$.
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