Question

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

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

3−3+3−4
3 to the negative 3 power plus 3 to the negative 4 power

32(3−5)
3 squared times open paren 3 to the negative 5 power close paren

3−11/3− superscript7

Answer 1

To find which expression simplifies to a positive exponent, let's analyze each option:

1. **−2(−3)²**
- Here, \((-3)^2 = 9\), so the expression simplifies to \(-2 \times 9 = -18\).
- This does not involve exponents in the final answer.

2. **3^(−3) + 3^(−4)**
- Both terms have negative exponents, so we can rewrite this as:
\[
\frac{1}{3^3} + \frac{1}{3^4} = \frac{1}{27} + \frac{1}{81}
\]
- This results in a positive value, but the exponents themselves are negative.

3. **3²(3^(−5))**
- Using the rule of exponents (\(a^m \cdot a^n = a^{m+n}\)):
\[
3^2 \cdot 3^{-5} = 3^{2-5} = 3^{-3}
\]
- This gives us a negative exponent.

4. **3^(−11) / 3^7**
- Using the rule of division with exponents (\(a^m / a^n = a^{m-n}\)):
\[
3^{-11} / 3^7 = 3^{-11-7} = 3^{-18}
\]
- This also results in a negative exponent.

Based on the analysis, none of these options directly simplify to a positive exponent. However, if the question is strictly looking for the expression that behaves closest to yielding positive results when fractions are calculated, but not on exponents itself, **Option 2 (3^(−3) + 3^(−4))** provides a positive result overall, even though it still involves negative exponents.

Thus, none of these expressions yield a strictly positive exponent after simplification. However, if just judging by summing fractions with negative exponents, it can be argued that **Option 2** is the least obstructive in terms of resulting in a positive outcome (this clarification is essential based on the nature of the question).

If you're seeking an expression that results in a positive exponent, you'd need to provide one where negative and positive exponents result in a net positive exponent. As it stands, none of the given choices fit that description.