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

Question

Responses

16=4⋅4
16 equals 4 times 4

16=8⋅8
16 equals 8 times 8

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

Answer 1

To simplify the expression \(1614\) using the base \(16\), we need to identify which factorization of \(16\) might make the process easier.

Let's break down each option:

1. 16 = 4 ⋅ 4: This is a valid factorization of \(16\).

2. 16 = 8 ⋅ 8: This is incorrect, as \(8 ⋅ 8 = 64\), not \(16\).

3. 16 = 2 ⋅ 2 ⋅ 2 ⋅ 2: This is also a valid factorization as \(2^4 = 16\).

4. 16 = 4 ⋅ 2 ⋅ 2: This is also correct because \(4 ⋅ 2 ⋅ 2 = 16\).

Now, to simplify \(1614\) effectively, it makes sense to use the factorization that allows us to break down the base into smaller components. Both 16 = 4 ⋅ 4 and 16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 can be useful depending on how we want to approach simplification.

However, 16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 (option 3) is the most straightforward for exponential simplification, as it directly leads to the power of \(2^4\).

Thus, the most beneficial factorization for simplifying \(1614\) would be:

16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 (or option 3 from your list).