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All even numbers have 2 as a factor, but no odd numbers do. The only even number that will appear as a factor in prime factorizations is 2, because it is the only even Prime number. Thus, an odd number will not have even numbers in its prime factorization because an odd number is not evenly divisible by 2.

The only even numbers that could appear in the exponential form are the exponents. For example 81 is 34. The factor is an odd number - 3, while the exponent is an even number - 4.

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Q: Will an odd number ever have even numbers in its exponential form?
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