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The powers of the prime factors in are added up to form:

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answer is D.

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Detailed Solution

Concept- Find each of the 108 and 192 prime factors separately first. (For instance, the prime factorization of 48 is

. Add the prime number powers with the same base (for instance,

). Then multiply both of the supplied numbers by their prime factors.
108 may be broken down into its prime factors, which are

and

when a is multiplied by itself n times.
Use the method above to add powers of numbers with the same base.
When aggregating powers of primes with the same base, the prime factorization of 108 can be written as

.
Prime factorization of 192 in step two is

Utilise the formula for adding powers from step 1 once again.
Prime factorization of 192 can be rewritten as

.
Write the prime factorization of

from steps 1 and 2.

For adding powers of numbers with the same base, use the formula above.

The prime elements of

are added together to form the sum.
(Prime Number Powers of 2) + (powers of prime number 3)

Therefore, 12 is the result of adding the powers of the

primes.
Hence, option 4 is correct.

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