Which factors of the base would help simplify the expression 1614?(1 point)

Question

Responses

16=4⋅2⋅2
16 equals 4 times 2 times 2

16=8⋅8
16 equals 8 times 8

16=4⋅4
16 equals 4 times 4

16=2⋅2⋅2⋅2

Answer 1

To simplify the expression \( 16^{14} \), we need to express 16 in terms of its prime factors. The correct factorization of 16 is:

\[ 16 = 2^4 \]

Now, we apply this factorization to \( 16^{14} \):

\[ 16^{14} = (2^4)^{14} = 2^{4 \cdot 14} = 2^{56} \]

Among the provided options, the factorization that would help simplify the expression \( 16^{14} \) is:

16 = 2⋅2⋅2⋅2 (since this shows the prime factor form as \( 2^4 \)).

This is the simplest way to express 16 in terms of its base factors, which ultimately leads to the simplification of \( 16^{14} \).