Question
Which factors of the base would help simplify the expression 1614
(1 point)
Responses
16 = 8*8
16 = 8*8
16 = 4*4
16 = 4*4
16 = 4*2*2
16 = 4*2*2
16 = 2*2*2*2
(1 point)
Responses
16 = 8*8
16 = 8*8
16 = 4*4
16 = 4*4
16 = 4*2*2
16 = 4*2*2
16 = 2*2*2*2
Answers
GPT-4o mini
To simplify the expression using the factors of the base 16, we need to consider the options provided:
1. \(16 = 8 \times 8\)
2. \(16 = 4 \times 4\)
3. \(16 = 4 \times 2 \times 2\)
4. \(16 = 2 \times 2 \times 2 \times 2\)
Out of these, the last representation, \(16 = 2 \times 2 \times 2 \times 2\) is particularly useful because it expresses 16 in terms of its prime factorization.
So the most effective factorization to simplify expressions involving base 16 would be:
**16 = 2 × 2 × 2 × 2**
This expresses 16 as a power of its prime base, which can aid in simplification if we are dealing with powers or roots.
For clarity, remember that \(a^b = (base)^{(exponent)}\) can drastically simplify expressions when the base is consistent, and finding the prime factors helps with that.
1. \(16 = 8 \times 8\)
2. \(16 = 4 \times 4\)
3. \(16 = 4 \times 2 \times 2\)
4. \(16 = 2 \times 2 \times 2 \times 2\)
Out of these, the last representation, \(16 = 2 \times 2 \times 2 \times 2\) is particularly useful because it expresses 16 in terms of its prime factorization.
So the most effective factorization to simplify expressions involving base 16 would be:
**16 = 2 × 2 × 2 × 2**
This expresses 16 as a power of its prime base, which can aid in simplification if we are dealing with powers or roots.
For clarity, remember that \(a^b = (base)^{(exponent)}\) can drastically simplify expressions when the base is consistent, and finding the prime factors helps with that.