Question

Which expression simplified would leave you with a negative exponent when simplified in exponent form?

-2(-3) to the second power
2 to the third power - 2 to the fourth power
2 to the negative twelfth power / 2 to the negative sixth power
2 to the fifth power times 2 to the negative second power

Answer 1

To find which expression simplified would leave you with a negative exponent when simplified in exponent form, let's evaluate each option:

1. **\(-2(-3)^2\)**:
\[
-2 \times 9 = -18
\]
This does not involve exponents after simplification, so it doesn't fit our criteria.

2. **\(2^3 - 2^4\)**:
\[
2^3 - 2^4 = 8 - 16 = -8
\]
This also does not involve exponents after simplification.

3. **\(\frac{2^{-12}}{2^{-6}}\)**:
Using the properties of exponents:
\[
\frac{2^{-12}}{2^{-6}} = 2^{-12 - (-6)} = 2^{-12 + 6} = 2^{-6}
\]
This expression results in a negative exponent.

4. **\(2^5 \times 2^{-2}\)**:
Again, using the properties of exponents:
\[
2^5 \times 2^{-2} = 2^{5 + (-2)} = 2^{5 - 2} = 2^3
\]
This results in a positive exponent.

From the evaluations, the expression that simplifies to have a negative exponent is **\(\frac{2^{-12}}{2^{-6}}\)**, which simplifies to \(2^{-6}\).