Question
Which expression simplified would leave you with a negative exponent when simplified in exponent form?(1 point)Responses−2(−3)2negative 2 times negative 3 squared23−242 cubed minus 2 to the 4th power25⋅2−22 to the 5th power times 2 to the negative 2 power2−122−6the fraction with numerator 2 to the negative 12 power and denominator 2 to the negative 6 power
Answers
GPT-4o mini
To determine which expression simplified would leave a negative exponent when in exponent form, let's evaluate each response option by simplifying them:
1. **−2(−3)²**
This simplifies to \(-2 \times 9 = -18\). No exponents involved.
2. **23−24**
This can be simplified to \(2^{3 - 4} = 2^{-1}\). This does result in a negative exponent.
3. **2³−2⁴**
This simplifies to \(2^3 - 2^4 = 8 - 16 = -8\). No exponents involved in this expression either.
4. **2⁵⋅2−2**
By using the property \(a^m \cdot a^n = a^{m+n}\), this simplifies to \(2^{5 - 2} = 2^3\). No negative exponent here.
5. **2−12/2−6**
Using the property of exponents \(\frac{a^m}{a^n} = a^{m - n}\), this simplifies to \(2^{-12 - (-6)} = 2^{-12 + 6} = 2^{-6}\). This also results in a negative exponent.
After evaluating all options, the ones that result in a negative exponent when simplified are:
- **2³−2⁴** (which simplifies to \(2^{-1}\))
- **2−12/2−6** (which simplifies to \(2^{-6}\))
So, the two right choices are responses **2** and **5**. But since the question seems to be looking for a single answer indicating that we'd like a negative exponent, the first one that enables that is:
**2³−2⁴ → 2^{-1}**
1. **−2(−3)²**
This simplifies to \(-2 \times 9 = -18\). No exponents involved.
2. **23−24**
This can be simplified to \(2^{3 - 4} = 2^{-1}\). This does result in a negative exponent.
3. **2³−2⁴**
This simplifies to \(2^3 - 2^4 = 8 - 16 = -8\). No exponents involved in this expression either.
4. **2⁵⋅2−2**
By using the property \(a^m \cdot a^n = a^{m+n}\), this simplifies to \(2^{5 - 2} = 2^3\). No negative exponent here.
5. **2−12/2−6**
Using the property of exponents \(\frac{a^m}{a^n} = a^{m - n}\), this simplifies to \(2^{-12 - (-6)} = 2^{-12 + 6} = 2^{-6}\). This also results in a negative exponent.
After evaluating all options, the ones that result in a negative exponent when simplified are:
- **2³−2⁴** (which simplifies to \(2^{-1}\))
- **2−12/2−6** (which simplifies to \(2^{-6}\))
So, the two right choices are responses **2** and **5**. But since the question seems to be looking for a single answer indicating that we'd like a negative exponent, the first one that enables that is:
**2³−2⁴ → 2^{-1}**