To simplify the expression 1614 by considering the factors of the base 16, you should focus on how 16 can be expressed in terms of its prime factors or simpler multiplication forms.
Here are the breakdowns of the options you provided:
- 16 = 4 * 4: This representation shows that 4 is a factor of 16.
- 16 = 8 * 8: This representation is incorrect because 8 * 8 equals 64, not 16.
- 16 = 2 * 2 * 2 * 2: This representation is correct as it expresses 16 in terms of its prime factorization (2^4).
- 16 = 4 * 2 * 2: This representation is also correct since 4 * 2 * 2 equals 16.
Among these options, the representation 16 = 2 * 2 * 2 * 2 is often the most useful for simplifying expressions, particularly in terms of handling powers.
Therefore, focusing on the factors of the base, 16 = 2 * 2 * 2 * 2 would be the most beneficial for simplification.