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

Question

Responses

16=4⋅4
16 equals 4 times 4

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

16=4⋅2⋅2
16 equals 4 times 2 times 2

16=8⋅8

Answer 1

To simplify the expression using the factors of the base \(16\), you need to express \(16\) in a way that reveals its prime factors. Let's analyze the options given:

1. \(16 = 4 \cdot 4\)
2. \(16 = 2 \cdot 2 \cdot 2 \cdot 2\)
3. \(16 = 4 \cdot 2 \cdot 2\)
4. \(16 = 8 \cdot 8\)

The most effective way to express \(16\) in terms of prime factors is option 2: \[ 16 = 2 \cdot 2 \cdot 2 \cdot 2 \] This can also be expressed as: \[ 16 = 2^4 \]

Using \(2^4\) is particularly helpful in simplifying expressions related to powers or exponential forms, since it allows for easier manipulation in calculations involving factors of \(16\).

Hence, the best response is: 16 = 2⋅2⋅2⋅2 (16 equals 2 times 2 times 2 times 2).