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

Question

Responses

16=8⋅8
16 equals 8 times 8

16=4⋅2⋅2
16 equals 4 times 2 times 2

16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2

16=4⋅4
16 equals 4 times 4

Answer 1

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

The factorization of \( 16 \) is:

• \( 16 = 2^4 \)

This means that we can rewrite \( 16^{14} \) as: \[ 16^{14} = (2^4)^{14} = 2^{4 \cdot 14} = 2^{56} \]

Among the provided options, the one that simplifies nicely and provides the necessary information is:

• 16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 (This demonstrates that \( 16 \) is made up of four \( 2 \)'s, which is the key for further simplification into powers of \( 2 \).)

So the correct response from the options given that would help simplify the expression is: 16=2⋅2⋅2⋅2 (16 equals 2 times 2 times 2 times 2).