Question
Which factors of the base would help simplify the expression 16 1/4?(1 point)
Responses
16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2
16=4⋅4
16 equals 4 times 4
16=8⋅8
16 equals 8 times 8
16=4⋅2⋅2
Responses
16=2⋅2⋅2⋅2
16 equals 2 times 2 times 2 times 2
16=4⋅4
16 equals 4 times 4
16=8⋅8
16 equals 8 times 8
16=4⋅2⋅2
Answers
GPT-4o mini
To simplify the expression \(16 \frac{1}{4}\), it may be beneficial to break down the whole number (16) into its prime factors or factorizations that relate directly to the fraction \( \frac{1}{4} \).
1. \( 16 = 2 \cdot 2 \cdot 2 \cdot 2 \) (this shows it's in terms of prime factors)
2. \( 16 = 4 \cdot 4 \) (this factorization is useful because \(4\) relates directly to the denominator of your fractional part)
3. \( 16 = 8 \cdot 8 \) (this isn't particularly useful in this context)
4. \( 16 = 4 \cdot 2 \cdot 2 \) (this is also relevant since it includes the factor \(4\))
The most direct factorization that would help simplify the expression \(16 \frac{1}{4}\) is:
**16 = 4 ⋅ 4**
This allows you to rewrite \( 16 \frac{1}{4} \) as \( 4 \cdot 4 + \frac{1}{4} \), which can be computed more easily. So the best factor for this context is \( 16 = 4 \cdot 4 \).
1. \( 16 = 2 \cdot 2 \cdot 2 \cdot 2 \) (this shows it's in terms of prime factors)
2. \( 16 = 4 \cdot 4 \) (this factorization is useful because \(4\) relates directly to the denominator of your fractional part)
3. \( 16 = 8 \cdot 8 \) (this isn't particularly useful in this context)
4. \( 16 = 4 \cdot 2 \cdot 2 \) (this is also relevant since it includes the factor \(4\))
The most direct factorization that would help simplify the expression \(16 \frac{1}{4}\) is:
**16 = 4 ⋅ 4**
This allows you to rewrite \( 16 \frac{1}{4} \) as \( 4 \cdot 4 + \frac{1}{4} \), which can be computed more easily. So the best factor for this context is \( 16 = 4 \cdot 4 \).