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

Question

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 determine which expression, when simplified, would leave a positive exponent, let’s evaluate each option:

1. −2(−3)²
   Simplifying gives:
   \(-2 \times (9) = -18\)
   This is a numerical value and does not involve exponents in simplified form.

2. 3⁻³ + 3⁻⁴
   This can be simplified by combining the terms:
   \(3^{-3} + 3^{-4} = 3^{-3} + 3^{-4} = 3^{-3}(1 + 3^{-1}) = 3^{-3}(1 + \frac{1}{3}) = 3^{-3} \cdot \frac{4}{3}\)
   This results in \( \frac{4}{3} \cdot 3^{-3} = \frac{4}{3} \cdot \frac{1}{3^3} \), which still includes a negative exponent.

3. 3²(3⁻⁵)
   Simplifying gives:
   \(3^{2 + (-5)} = 3^{-3}\)
   This, again, has a negative exponent.

4. 3⁻¹/3⁷
   This can be simplified using the property of exponents:
   \( \frac{3^{-1}}{3^{7}} = 3^{-1 - 7} = 3^{-8}\)
   This also results in a negative exponent.

From the above evaluations, none of these expressions simplify to a positive exponent.

However, if the question allowed for rewriting or factoring, you could potentially rewrite an expression to yield a positive exponent. For the options given as they are, they all yield negative exponents when simplified. If you are meant to pick one that may suggest a move towards positivity or is a trick question, you might reconsider the context or recheck for an error in interpretation.

Please confirm if any clarification on the expectations of the answer is needed!