Question

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

2^3−2^4
2 cubed minus 2 to the 4th power

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

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

−2(−3)^2

Answer 1

To determine which expression simplifies to a negative exponent, we can simplify each option.

1. **\(2^3 - 2^4\)**:
- This does not simplify to an exponent but rather is a numerical expression: \(2^3 = 8\) and \(2^4 = 16\), so \(8 - 16 = -8\). No exponent is involved.

2. **\(2^5 \cdot 2^{-2}\)**:
- Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\):
\[
2^5 \cdot 2^{-2} = 2^{5 + (-2)} = 2^{5 - 2} = 2^3
\]
- This results in a positive exponent, \(2^3\).

3. **\(\frac{2^{-12}}{2^{-6}}\)**:
- Using the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\):
\[
\frac{2^{-12}}{2^{-6}} = 2^{-12 - (-6)} = 2^{-12 + 6} = 2^{-6}
\]
- This expression does simplify to a negative exponent, \(2^{-6}\).

4. **\(-2(-3)^2\)**:
- This is a numerical expression:
\[
-2 \cdot 9 = -18
\]
- No exponent involved.

From the above options, the expression that simplifies to contain a negative exponent is:

**\(\frac{2^{-12}}{2^{-6}}\)**, which simplifies to \(2^{-6}\).