Question
Iris found a value of 164
when she evaluated an expression. Which could have been the expression Iris evaluated? Check the two that apply.(2 points)
Responses
4−3
4 to the negative 3 power
6−4
6 to the negative 4 power
2−6
2 to the negative 6 power
(14)−3
1 fourth to the negative 3 power
(12)−5
when she evaluated an expression. Which could have been the expression Iris evaluated? Check the two that apply.(2 points)
Responses
4−3
4 to the negative 3 power
6−4
6 to the negative 4 power
2−6
2 to the negative 6 power
(14)−3
1 fourth to the negative 3 power
(12)−5
Answers
GPT-4o mini
To determine which of the expressions could have resulted in the value of 164, we need to evaluate each expression. The numbers are treated in different manners when using the negative exponent notation:
1. **4−3**: This is \(4 - 3 = 1\).
2. **4 to the negative 3 power**: This is \(4^{-3} = \frac{1}{4^3} = \frac{1}{64} \approx 0.015625\).
3. **6−4**: This is \(6 - 4 = 2\).
4. **6 to the negative 4 power**: This is \(6^{-4} = \frac{1}{6^4} = \frac{1}{1296} \approx 0.0007716\).
5. **2−6**: This is \(2 - 6 = -4\).
6. **2 to the negative 6 power**: This is \(2^{-6} = \frac{1}{2^6} = \frac{1}{64} \approx 0.015625\).
7. **(14)−3**: This is \(14 - 3 = 11\).
8. **1 fourth to the negative 3 power**: This is \((\frac{1}{4})^{-3} = 4^3 = 64\).
9. **(12)−5**: This is \(12 - 5 = 7\).
After evaluating all the expressions, none of them equal 164 when calculated directly. Therefore, it appears that none of these options could be the expression Iris evaluated.
If there is a different way you want to consider these options or if there are more options available, please let me know!
1. **4−3**: This is \(4 - 3 = 1\).
2. **4 to the negative 3 power**: This is \(4^{-3} = \frac{1}{4^3} = \frac{1}{64} \approx 0.015625\).
3. **6−4**: This is \(6 - 4 = 2\).
4. **6 to the negative 4 power**: This is \(6^{-4} = \frac{1}{6^4} = \frac{1}{1296} \approx 0.0007716\).
5. **2−6**: This is \(2 - 6 = -4\).
6. **2 to the negative 6 power**: This is \(2^{-6} = \frac{1}{2^6} = \frac{1}{64} \approx 0.015625\).
7. **(14)−3**: This is \(14 - 3 = 11\).
8. **1 fourth to the negative 3 power**: This is \((\frac{1}{4})^{-3} = 4^3 = 64\).
9. **(12)−5**: This is \(12 - 5 = 7\).
After evaluating all the expressions, none of them equal 164 when calculated directly. Therefore, it appears that none of these options could be the expression Iris evaluated.
If there is a different way you want to consider these options or if there are more options available, please let me know!