Question

Which expression simplified would leave you with a negative exponent when simplified in exponent form?(1 point)
Responses

−2(−3)2
negative 2 times negative 3 squared

25⋅2−2
2 to the 5th power times 2 to the negative 2 power

2−122−6
the fraction with numerator 2 to the negative 12 power and denominator 2 to the negative 6 power

23−24

Answer 1

To find which expression simplifies to a negative exponent when expressed in exponent form, let's analyze each option:

1. **−2(−3)²**
This evaluates to \(-2 \times 9\) which equals \(-18\). No exponent involved.

2. **25⋅2−2**
This remains as \(2^5 \times 2^{-2}\), and according to the laws of exponents, that simplifies to:
\[
2^{5 + (-2)} = 2^{3}
\]
No negative exponent here.

3. **2−12/2−6**
This simplifies as follows:
\[
2^{-12} \div 2^{-6} = 2^{-12 - (-6)} = 2^{-12 + 6} = 2^{-6}
\]
This results in a negative exponent (-6).

4. **23−24**
This simplifies using the laws of exponents:
\[
2^3 - 2^4 = 2^{3 - 4} = 2^{-1}
\]
This also results in a negative exponent (-1).

From the analysis above, both options 3 and 4 yield a negative exponent. However, since only one answer can be selected and option 3 explicitly simplifies to a negative exponent format, that is the primary option to choose.

**Final answer:** **2⁻¹²/2⁻⁶** which simplifies to **2⁻⁶**.