To simplify the expression \( 1614 \) based on the factors of the base 16, we can express 16 in its prime factorization. The factorization of 16 is:
\[ 16 = 2^4 \]
This means that when working with the base of 16, you can simplify expressions involving powers of 16 by expressing them in terms of its prime factors (i.e., in terms of base 2).
Here are the provided options:
- \( 16 = 8*8 \)
- \( 16 = 4*4 \)
- \( 16 = 422 \)
- \( 16 = 222*2 \)
To determine which of these factorizations would help simplify the expression based on base 16, we note that all these factorizations are ultimately linked to the powers of 2. However, since 16 itself is most simply expressed as \( 2^4 \), the last option \( 16 = 222*2 \) most directly represents its prime factors.
Thus, the factorization that would be most helpful in simplifying the expression in terms of base 16 would be:
\[ 16 = 222*2 \]
This representation clearly shows the base raised to a power, which is useful when simplifying powers of 16.