To simplify the expression \( 16^{14} \), we can start by expressing 16 in terms of its prime factorization.
The number \( 16 \) can be expressed as: \[ 16 = 2^4 \]
Thus, we can rewrite \( 16^{14} \): \[ 16^{14} = (2^4)^{14} \]
Using the power of a power property of exponents, we multiply the exponents: \[ (2^4)^{14} = 2^{4 \cdot 14} = 2^{56} \]
Therefore, the simplified expression for \( 16^{14} \) is: \[ 2^{56} \]
To answer your question about which factors of the base would help simplify the expression, we can see that breaking down \( 16 \) in terms of its prime factorization \( 16 = 2^4 \) is key to simplifying \( 16^{14} \) to \( 2^{56} \).
If you are looking for the possible responses based on the choices given, it seems you're seeking to identify representations of that simplification process, specifically through the prime factorization of 16.
From the choices you provided, \( 16 = 2 \cdot 2 \cdot 2 \cdot 2 \) directly corresponds to the prime factorization and is appropriate for simplifying \( 16^{14} \).
Thus, the best response to "which factors of the base would help simplify" \( 16^{14} \) is: \[ 16 = 2 \cdot 2 \cdot 2 \cdot 2 \]