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− superscript11/3− superscript7

Answer 1

To determine which expression simplifies to leave a positive exponent, let's simplify each option one by one:

1. −2(−3)²

   • This simplifies to \(-2 \cdot 9 = -18\), which does not involve exponents in the final result.

2. 3⁻³ + 3⁻⁴

   • This can be rewritten as \(\frac{1}{3³} + \frac{1}{3⁴}\).
   • Finding a common denominator: \(\frac{3}{3⁴} + \frac{1}{3⁴} = \frac{3 + 1}{3⁴} = \frac{4}{3⁴} = 4 \cdot 3⁻⁴\).
   • This expression still has a negative exponent (specifically \(3^{-4}\)).

3. 32(3⁻⁵)

   • This simplifies to \(9 \cdot 3^{-5} = 9/3^5\), which can be expressed as \(9/243\) but also still has a negative exponent.

4. 3⁻(11/3) − 3⁻(7)

   • Here, we can rewrite this as \(3^{-11/3} - 3^{-7}\).
   • Informally, we can factor out a common term if we consider them on a common base; however, both terms retain negative exponents after simplification.

The only expression that results in a simplified version that does not retain any negative exponents requires reviewing this question's specific requirements.

None of the provided expressions end up resulting with a positive exponent when fully simplified.

Please double-check the specific context or any possible miscommunication about the task, as, based on standard exponent rules, none of the options yield a purely positive exponent in the final simplified form provided above.