Question
Which expressions are equivalent to -64? Check TWO that apply.(2 points)
Responses
4−3
4 to the negative 3 power
−(14)−3
negative 1 fourth to the negative 3 power
28−2422
the fraction with numerator 2 to the 8th power minus 2 to the 4th power and denominator 2 squared
23⋅22⋅20
2 cubed times 2 squared times 2 to the 0 power
−2 − superscript2 ⋅ ( 2 superscript8 )
Responses
4−3
4 to the negative 3 power
−(14)−3
negative 1 fourth to the negative 3 power
28−2422
the fraction with numerator 2 to the 8th power minus 2 to the 4th power and denominator 2 squared
23⋅22⋅20
2 cubed times 2 squared times 2 to the 0 power
−2 − superscript2 ⋅ ( 2 superscript8 )
Answers
GPT-4o mini
To determine which expressions are equivalent to -64, we will evaluate each of them.
1. **4−3** (4 to the negative 3 power):
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64} \quad \text{(not -64)}
\]
2. **−(14)−3** (negative 1 fourth to the negative 3 power):
\[
-\left(\frac{1}{4}\right)^{-3} = -4^3 = -64 \quad \text{(this equals -64)}
\]
3. **28−2422** (the fraction with numerator \(2^8 - 2^4\) and denominator \(2^2\)):
\[
= \frac{2^8 - 2^4}{2^2} = \frac{256 - 16}{4} = \frac{240}{4} = 60 \quad \text{(not -64)}
\]
4. **23⋅22⋅20** (2 cubed times 2 squared times 2 to the 0 power):
\[
2^3 \cdot 2^2 \cdot 2^0 = 2^{3+2+0} = 2^5 = 32 \quad \text{(not -64)}
\]
5. **−2 − superscript2 ⋅ ( 2 superscript8 )** (-2 squared times \(2^8\)):
\[
-2^2 \cdot 2^8 = -4 \cdot 256 = -1024 \quad \text{(not -64)}
\]
Based on the evaluations, the expressions that are equivalent to -64 are:
1. **−(14)−3**
Thus, the expression that applies is:
- **−(14)−3** (this one equals -64).
There is only one correct answer from the provided options that equals -64. It seems that there is no second option that correctly evaluates to -64 based on the given expressions. Therefore, the only correct answer is:
- **−(14)−3**.
1. **4−3** (4 to the negative 3 power):
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64} \quad \text{(not -64)}
\]
2. **−(14)−3** (negative 1 fourth to the negative 3 power):
\[
-\left(\frac{1}{4}\right)^{-3} = -4^3 = -64 \quad \text{(this equals -64)}
\]
3. **28−2422** (the fraction with numerator \(2^8 - 2^4\) and denominator \(2^2\)):
\[
= \frac{2^8 - 2^4}{2^2} = \frac{256 - 16}{4} = \frac{240}{4} = 60 \quad \text{(not -64)}
\]
4. **23⋅22⋅20** (2 cubed times 2 squared times 2 to the 0 power):
\[
2^3 \cdot 2^2 \cdot 2^0 = 2^{3+2+0} = 2^5 = 32 \quad \text{(not -64)}
\]
5. **−2 − superscript2 ⋅ ( 2 superscript8 )** (-2 squared times \(2^8\)):
\[
-2^2 \cdot 2^8 = -4 \cdot 256 = -1024 \quad \text{(not -64)}
\]
Based on the evaluations, the expressions that are equivalent to -64 are:
1. **−(14)−3**
Thus, the expression that applies is:
- **−(14)−3** (this one equals -64).
There is only one correct answer from the provided options that equals -64. It seems that there is no second option that correctly evaluates to -64 based on the given expressions. Therefore, the only correct answer is:
- **−(14)−3**.