Question
Which expression simplified would leave you with a positive exponent when simplified in exponent form?
-2(-3) to the second power
3 to the negative third power + 3 to the negative fourth power
3 to the second power(3 to the negative fifth power)
3 to the negative eleventh power / 3 to the negative seventh power
-2(-3) to the second power
3 to the negative third power + 3 to the negative fourth power
3 to the second power(3 to the negative fifth power)
3 to the negative eleventh power / 3 to the negative seventh power
Answers
GPT-4o mini
To determine which expression, when simplified, would have a positive exponent, let's analyze each option one by one.
1. **\(-2(-3)^{2}\)**:
- Calculate \((-3)^{2}\):
\[ (-3)^{2} = 9 \]
- Thus, the expression becomes:
\[ -2 \times 9 = -18 \]
There are no exponents involved in this final answer.
2. **\(3^{-3} + 3^{-4}\)**:
- These can be combined since they have the same base:
\[ 3^{-3} + 3^{-4} = 3^{-4}(3^{-(-3 + 4)} + 1) = 3^{-4}(3^1 + 1) \]
\[ = 3^{-4}(3 + 1) = 3^{-4}(4) = \frac{4}{3^{4}} \]
The result here has a negative exponent.
3. **\(3^{2}(3^{-5})\)**:
- When multiplying with the same base, we can add the exponents:
\[ 3^{2} \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3} \]
The result has a negative exponent.
4. **\(\frac{3^{-11}}{3^{-7}}\)**:
- When dividing with the same base, we subtract the exponents:
\[ \frac{3^{-11}}{3^{-7}} = 3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4} \]
This also results in a negative exponent.
After analyzing all the options, none of them simplify to a positive exponent. It appears that no expressions in the provided options simplify to a positive exponent.
1. **\(-2(-3)^{2}\)**:
- Calculate \((-3)^{2}\):
\[ (-3)^{2} = 9 \]
- Thus, the expression becomes:
\[ -2 \times 9 = -18 \]
There are no exponents involved in this final answer.
2. **\(3^{-3} + 3^{-4}\)**:
- These can be combined since they have the same base:
\[ 3^{-3} + 3^{-4} = 3^{-4}(3^{-(-3 + 4)} + 1) = 3^{-4}(3^1 + 1) \]
\[ = 3^{-4}(3 + 1) = 3^{-4}(4) = \frac{4}{3^{4}} \]
The result here has a negative exponent.
3. **\(3^{2}(3^{-5})\)**:
- When multiplying with the same base, we can add the exponents:
\[ 3^{2} \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3} \]
The result has a negative exponent.
4. **\(\frac{3^{-11}}{3^{-7}}\)**:
- When dividing with the same base, we subtract the exponents:
\[ \frac{3^{-11}}{3^{-7}} = 3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4} \]
This also results in a negative exponent.
After analyzing all the options, none of them simplify to a positive exponent. It appears that no expressions in the provided options simplify to a positive exponent.